/*
 This file is part of Nenofex.

 Nenofex, an expansion-based QBF solver for negation normal form.        
 Copyright 2008, 2012, 2017 Florian Lonsing.

 Nenofex is free software: you can redistribute it and/or modify
 it under the terms of the GNU General Public License as published by
 the Free Software Foundation, either version 3 of the License, or (at
 your option) any later version.

 Nenofex is distributed in the hope that it will be useful, but
 WITHOUT ANY WARRANTY; without even the implied warranty of
 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
 General Public License for more details.

 You should have received a copy of the GNU General Public License
 along with Nenofex.  If not, see <http://www.gnu.org/licenses/>.
*/

#include <stdio.h>
#include <string.h>
#include <assert.h>
#include <stdlib.h>
#include <ctype.h>
#include <limits.h>
#include <math.h>
#include <picosat.h>
#include "nenofex_types.h"
#include "stack.h"
#include "mem.h"

/*
- wrapper-macros for calling internal SAT-solver
*/
#define sat_solver_init(N) ((N)->picosat = picosat_init())
#define sat_solver_verbosity_mode(N) (picosat_set_verbosity((N)->picosat, 1))
#define sat_solver_reset(N) (picosat_reset((N)->picosat))
#define sat_solver_add(N,lit) (picosat_add((N)->picosat,(lit)))
#define sat_solver_sat(N) (picosat_sat((N)->picosat,(N)->options.sat_solver_dec_limit > 0 ? \
                                       (N)->options.sat_solver_dec_limit : -1))
#define sat_solver_deref(N,lit) (picosat_deref((N)->picosat,lit))
#define SAT_SOLVER_RESULT_UNKNOWN PICOSAT_UNKNOWN
#define SAT_SOLVER_RESULT_SATISFIABLE PICOSAT_SATISFIABLE
#define SAT_SOLVER_RESULT_UNSATISFIABLE PICOSAT_UNSATISFIABLE


/*
- full-scale assertion checking
- involves full traversals of whole graph, occurrence lists,...
- VERY expensive!
- flag 'NDEBUG' overules any setting of the following
*/
#if 1

#define ASSERT_AFTER_EXP_ALL_NON_INNERMOST_SCOPE_VARS_UNINIT 0
#define ASSERT_BEFORE_FIND_VAR_CCA_FULL_GRAPH_INTEGRITY 0
#define ASSERT_AFTER_FIND_VAR_LCA_FULL_GRAPH_INTEGRITY 0

#define ASSERT_LCA_OBJECT_INTEGRITY 0
#define ASSERT_ALL_LCA_CHILDREN_UNMARKED 0

#define ASSERT_COPY_EQUALS 0

#define ASSERT_SIZES_IN_EXPANSION 0
#define PRINT_SIZE_CHECK_INFO 0

#define ASSERT_GRAPH_AFTER_EXP_BEFORE_PROP 0
#define ASSERT_GRAPH_AFTER_EXP_AFTER_PROP 0

#define ASSERT_GRAPH_AFTER_ATPG_GLOBAL_FLOW 0

#define ASSERT_GRAPH_BETWEEN_DEC_SCORE 0
#define ASSERT_GRAPH_AFTER_DEC_SCORE 0
#define ASSERT_INIT_SCOPE_SCORES_ALL_UNMARKED 0
#define ASSERT_INIT_VAR_SCORES_ALL_UNMARKED 0
#define ASSERT_GRAPH_AFTER_PARSING 0
#define ASSERT_SIMP_ONE_LEVEL_BEFORE 0

#define ASSERT_POS_IN_CHANGED_CH_LIST 0

#define ASSERT_PRIORITY_QUEUE_HEAP_CONDITION 0
#define ASSERT_ALL_SCOPES_FREE_OF_NO_OCC_VARS 0
#define ASSERT_ALL_SCOPES_PRIORITY_QUEUE_HEAP_CONDITION 0

#define ASSERT_UNIVERSAL_LCA_COMPUTATION_GRAPH_AND_VARS 0
#define ASSERT_PREPARE_NON_INNERMOST_UNIVERSAL_EXPANSION 0
#define ASSERT_ALL_DEPENDING_VARS_CLEANED_UP 0
#define DELETE_ELEM_ASSERT_PRIORITY_QUEUE_HEAP_CONDITION 0

#define ASSERT_SCOPE_VAR_CNT 0

#define ASSERT_POST_EXPANSION_FLATTENING 0

#define ASSERT_ALL_LCA_OCC_POS_INTEGRITY 0

#else

#define ASSERT_AFTER_EXP_ALL_NON_INNERMOST_SCOPE_VARS_UNINIT 1
#define ASSERT_BEFORE_FIND_VAR_LCA_FULL_GRAPH_INTEGRITY 1
#define ASSERT_AFTER_FIND_VAR_LCA_FULL_GRAPH_INTEGRITY 1
#define ASSERT_LCA_OBJECT_INTEGRITY 1
#define ASSERT_ALL_LCA_CHILDREN_UNMARKED 1
#define ASSERT_COPY_EQUALS 1
#define ASSERT_SIZES_IN_EXPANSION 1
#define PRINT_SIZE_CHECK_INFO 0
#define ASSERT_GRAPH_AFTER_EXP_BEFORE_PROP 1
#define ASSERT_GRAPH_AFTER_EXP_AFTER_PROP 1

#define ASSERT_GRAPH_AFTER_ATPG_GLOBAL_FLOW 1

#define ASSERT_GRAPH_BETWEEN_DEC_SCORE 1
#define ASSERT_GRAPH_AFTER_DEC_SCORE 1
#define ASSERT_INIT_SCOPE_SCORES_ALL_UNMARKED 1
#define ASSERT_INIT_VAR_SCORES_ALL_UNMARKED 1
#define ASSERT_GRAPH_AFTER_PARSING 1
#define ASSERT_SIMP_ONE_LEVEL_BEFORE 1

#define ASSERT_POS_IN_CHANGED_CH_LIST 1

#define ASSERT_PRIORITY_QUEUE_HEAP_CONDITION 1
#define ASSERT_ALL_SCOPES_FREE_OF_NO_OCC_VARS 1
#define ASSERT_ALL_SCOPES_PRIORITY_QUEUE_HEAP_CONDITION 1

#define ASSERT_UNIVERSAL_LCA_COMPUTATION_GRAPH_AND_VARS 1
#define ASSERT_PREPARE_NON_INNERMOST_UNIVERSAL_EXPANSION 1
#define ASSERT_ALL_DEPENDING_VARS_CLEANED_UP 1
#define DELETE_ELEM_ASSERT_PRIORITY_QUEUE_HEAP_CONDITION 1

#define ASSERT_SCOPE_VAR_CNT 1

#define ASSERT_POST_EXPANSION_FLATTENING 1

#define ASSERT_ALL_LCA_OCC_POS_INTEGRITY 1

#endif /* end: full-scale assertion checking */


/*
- print info about number of updated and remaining vars after each expansion
*/
#define PRINT_INCREMENTAL_COST_UPDATE 0


/*
- compute statistics after each expansion and print to 'stderr'
- rather expensive (full traversal of graph)
*/
#define COMPUTE_GRAPH_STATISTICS 0


/*
- print number of clauses that would be generated by revised tseitin transf.
- rather expensive!
- FOR CNFs ONLY: WILL RAISE ASSERTION FAILURE IF CALLED ON QBFs!
*/
#define PRINT_CLAUSE_COUNT 0


#define PRINT_LIT_STATS_BEFORE_EXP 0
#define ASSERT_PRINT_LIT_STATS_BEFORE_EXP 0


/* optional statistics */
#define COMPUTE_MAX_TREE_SIZE 1
#if 0
#define COMPUTE_NUM_DELETED_NODES 1
#define COMPUTE_NUM_NON_INC_EXPANSIONS_IN_SCORES 1
#define COMPUTE_NUM_NON_INC_EXPANSIONS 1
#define COMPUTE_CASES_IN_EXPANSIONS 1
#define COMPUTE_AVERAGE_UPDATE_MARKED_RATIOS 1
#define COMPUTE_NUM_UNITS 1
#define COMPUTE_NUM_UNATES 1
#define COMPUTE_NUM_TOTAL_CREATED_NODES 1
#define COMPUTE_LCA_PARENT_VISITS 1
#endif
/* END: OPTIONAL STATISTICS */


/* 
- minor fix for opt-subgraph size reduction: ensure max. size of subgraph 
- enabling recommended, since this behaviour is wanted
*/
#define MAXIMIZE_REDUCED 1


/* delete pos-lists in nodes when empty */
#define DELETE_EMPTY_STACKS_IN_NODES 1


/* pick non-innermost universal variable with fewest literals */
#define APPROXIMATE_UNIV_SCORES 0


#define DEFAULT_STACK_SIZE 128
#define DEFAULT_QUEUE_SIZE 128
#define DEFAULT_SCOPE_NESTING INT_MAX


#define LCA_CHILDREN_INIT_SIZE 16


/*
- marking
*/
#define SIMPLIFY_VAR_POS_MARK 1
#define SIMPLIFY_VAR_NEG_MARK 2
#define simplify_var_marked(var) ((var)->simp_mark)
#define simplify_var_unmark(var) ((var)->simp_mark = 0)
#define simplify_var_pos_marked(var) ((var)->simp_mark == SIMPLIFY_VAR_POS_MARK)
#define simplify_var_neg_marked(var) ((var)->simp_mark == SIMPLIFY_VAR_NEG_MARK)
#define simplify_var_pos_mark(var) ((var)->simp_mark = SIMPLIFY_VAR_POS_MARK)
#define simplify_var_neg_mark(var) ((var)->simp_mark = SIMPLIFY_VAR_NEG_MARK)

/* #ifndef NDEBUG */
#define size_subformula_marked(node) ((node)->mark3)
#define size_subformula_mark(node) ((node)->mark3 = 1)
#define size_subformula_unmark(node) ((node)->mark3 = 0)
/* #endif */

#define lca_child_marked(node) ((node)->mark2)
#define mark_lca_child(node) ((node)->mark2 =  1)
#define unmark_lca_child(node) ((node)->mark2 = 0)

#define universal_lca_child_marked(node) ((node)->mark3)
#define mark_universal_lca_child(node) ((node)->mark3 = 1)
#define unmark_universal_lca_child(node) ((node)->mark3 = 0)

#define dependency_visit_marked(node) ((node)->mark1)
#define mark_dependency_visit(node) ((node)->mark1 = 1)
#define unmark_dependency_visit(node) ((node)->mark1 = 0)

/*
- operator nodes are marked during copying
*/
#define copy_formula_marked(node) ((node)->mark2)
#define copy_formula_mark(node) ((node)->mark2 = 1)
#define copy_formula_unmark(node) ((node)->mark2 = 0)

/*
- literals are marked during expansion
*/
#define truth_propagation_marked(node) ((node)->mark2)
#define truth_propagation_mark(node) ((node)->mark2 = 1)
#define truth_propagation_unmark(node) ((node)->mark2 = 0)

#define cost_update_marked(var) \
(((var)->lca_update_mark) || ((var)->inc_score_update_mark) \
   || ((var)->dec_score_update_mark))

#define decrease_score_marked(node) ((node)->mark1)
#define decrease_score_mark(node) ((node)->mark1 = 1)
#define decrease_score_unmark(node) ((node)->mark1 = 0)

#define decrease_score_collected_marked(node) ((node)->mark2)
#define decrease_score_collected_mark(node) ((node)->mark2 = 1)
#define decrease_score_collected_unmark(node) ((node)->mark2 = 0)


/* END: MACROS, CONFIGURATION */


/* ---------- START: PRIORITY QUEUE ---------- */

static void
create_priority_queue (MemManager *mm, Stack ** priority_heap, unsigned int init_capacity)
{
  *priority_heap = create_stack (mm, init_capacity);
}


static void
delete_priority_queue (MemManager *mm, Stack ** priority_heap)
{
  delete_stack (mm, *priority_heap);
  *priority_heap = 0;
}


static void
add_fast_priority_queue (MemManager *mm, Stack * priority_heap, Var * var)
{
  assert (var->priority_pos == -1);

  push_stack (mm, priority_heap, var);
  var->priority_pos = count_stack (priority_heap) - 1;

  assert (var->priority_pos >= 0);
  assert ((unsigned int) var->priority_pos < count_stack (priority_heap));
}


static int
get_left_child_pos (int cur_pos, int size)
{
  assert (cur_pos >= 0);
  assert (cur_pos < size);

  int result;

  result = 2 * cur_pos + 1;

  return result;
}


static int
get_right_child_pos (int cur_pos, int size)
{
  assert (cur_pos >= 0);
  assert (cur_pos < size);

  int result;

  result = 2 * (cur_pos + 1);

  return result;
}


static int
get_parent_pos (int cur_pos, int size)
{
  assert (cur_pos > 0);
  assert (cur_pos < size);

  int result;

  result = (cur_pos - 1) / 2;

  assert (result < size);

  assert (cur_pos == get_right_child_pos (result, size) ||
          cur_pos == get_left_child_pos (result, size));

  return result;
}


#ifndef NDEBUG
static void
assert_priority_queue_heap_condition (Stack * priority_heap)
{
  int size = count_stack (priority_heap);

  void **start = priority_heap->elems;

  int pos, no_children, left_child_pos, right_child_pos;
  no_children = size / 2;

  for (pos = 0; pos < size; pos++)
    {
      Var *cur_var, *left_var, *right_var;

      cur_var = start[pos];
      assert (cur_var->priority_pos == pos);

      left_child_pos = get_left_child_pos (pos, size);
      right_child_pos = get_right_child_pos (pos, size);

      if (pos < no_children)
        {
          assert (left_child_pos < size);

          left_var = start[left_child_pos];

          if (right_child_pos < size)
            right_var = start[right_child_pos];

          assert (cur_var->exp_costs.score <= left_var->exp_costs.score);
          assert (right_child_pos >= size ||
                  cur_var->exp_costs.score <= right_var->exp_costs.score);
        }
      else                      /* has no children */
        {
          assert (right_child_pos >= size);
          assert (left_child_pos >= size);
        }
    }                           /* end: for */

}
#endif


static int
compare_priority_queue (Stack * priority_heap, int pos_a, int pos_b)
{
  assert (pos_a >= 0);
  assert ((unsigned int) pos_a < count_stack (priority_heap));
  assert (pos_b >= 0);
  assert ((unsigned int) pos_b < count_stack (priority_heap));

  int result;

  void **start = priority_heap->elems;

  Var *var_a = start[pos_a];
  Var *var_b = start[pos_b];

  int var_a_score = var_a->exp_costs.score;
  int var_b_score = var_b->exp_costs.score;

  if (var_a_score < var_b_score)
    result = -1;
  else if (var_a_score == var_b_score)
    result = 0;
  else
    result = 1;

  return result;
}


static void
swap_priority_queue (Stack * priority_heap, int pos_a, int pos_b)
{
  assert (pos_a != pos_b);
  assert ((unsigned int) pos_a < count_stack (priority_heap));
  assert ((unsigned int) pos_b < count_stack (priority_heap));

  void **a, **b, **start;

  start = priority_heap->elems;

  a = start + pos_a;
  b = start + pos_b;

  Var *var_a, *var_b;

  var_a = *a;
  var_b = *b;

  assert (var_a->priority_pos == pos_a);
  assert (var_b->priority_pos == pos_b);

  *a = var_b;
  var_b->priority_pos = pos_a;

  *b = var_a;
  var_a->priority_pos = pos_b;
}


static void
up_heap (Stack * priority_heap, int cur_pos)
{
  int size = count_stack (priority_heap);

  assert (cur_pos < size);

  while (cur_pos > 0)
    {
      int parent_pos = get_parent_pos (cur_pos, size);

      if (compare_priority_queue (priority_heap, cur_pos, parent_pos) >= 0)
        break;

      swap_priority_queue (priority_heap, cur_pos, parent_pos);
      cur_pos = parent_pos;
    }                           /* end: while top not reached */
}


static void
down_heap (Stack * priority_heap, int cur_pos)
{
  int child_pos, left_child_pos, right_child_pos;
  int size = count_stack (priority_heap);

  assert (cur_pos >= 0);
  assert (cur_pos < size);

  for (;;)
    {
      left_child_pos = get_left_child_pos (cur_pos, size);

      if (left_child_pos >= size)
        break;                  /* has no left child */

      right_child_pos = get_right_child_pos (cur_pos, size);

      if (right_child_pos < size &&
          compare_priority_queue (priority_heap, left_child_pos,
                                  right_child_pos) > 0)
        child_pos = right_child_pos;
      else
        child_pos = left_child_pos;

      if (compare_priority_queue (priority_heap, cur_pos, child_pos) > 0)
        {
          swap_priority_queue (priority_heap, cur_pos, child_pos);
          cur_pos = child_pos;
        }
      else
        break;
    }                           /* end: for */
}


static void
init_order_priority_queue (Stack * priority_heap)
{
  int cur_pos, end_pos = count_stack (priority_heap);

  for (cur_pos = 0; cur_pos < end_pos; cur_pos++)
    {
      up_heap (priority_heap, cur_pos);
    }

#ifndef NDEBUG
#if ASSERT_PRIORITY_QUEUE_HEAP_CONDITION
  assert_priority_queue_heap_condition (priority_heap);
#endif
#endif
}


static void
delete_elem_priority_queue (Stack * priority_heap, int elem_pos)
{
  assert (elem_pos >= 0);
  assert ((unsigned int) elem_pos < count_stack (priority_heap));

#ifndef NDEBUG
#if DELETE_ELEM_ASSERT_PRIORITY_QUEUE_HEAP_CONDITION
  assert_priority_queue_heap_condition (priority_heap);
#endif
#endif

  Var *last, *del;
  void **pos = priority_heap->elems + elem_pos;

  del = *pos;
  assert (del->priority_pos == elem_pos);
  del->priority_pos = -1;

  last = pop_stack (priority_heap);

  if (del != last)
    {
      *pos = last;
      last->priority_pos = elem_pos;
      up_heap (priority_heap, elem_pos);
      down_heap (priority_heap, elem_pos);
    }

#ifndef NDEBUG
#if DELETE_ELEM_ASSERT_PRIORITY_QUEUE_HEAP_CONDITION
  assert_priority_queue_heap_condition (priority_heap);
#endif
#endif
}


static Var *
remove_min (Stack * priority_heap)
{
  void **start = priority_heap->elems;

  if (start == priority_heap->top)
    return 0;

  Var *min_var, *last_var;

  min_var = *start;
  min_var->priority_pos = -1;

  last_var = pop_stack (priority_heap);

  assert (last_var != min_var || count_stack (priority_heap) == 0);

  if (min_var == last_var)
    return min_var;

  *start = last_var;
  last_var->priority_pos = 0;

  if (count_stack (priority_heap) >= 2)
    {
      down_heap (priority_heap, 0);
    }

#ifndef NDEBUG
#if ASSERT_PRIORITY_QUEUE_HEAP_CONDITION
  assert_priority_queue_heap_condition (priority_heap);
#endif
#endif

  return min_var;
}


static Var *
access_min (Stack * priority_heap)
{
  void **start = priority_heap->elems;

  if (start == priority_heap->top)
    return 0;
  else
    return *start;
}


static void
decrease_key (Stack * priority_heap, Var * var)
{
  int cur_pos = var->priority_pos;

  assert (cur_pos >= 0);
  assert ((unsigned int) cur_pos < count_stack (priority_heap));
  assert (var == priority_heap->elems[cur_pos]);

  up_heap (priority_heap, cur_pos);
}


static void
increase_key (Stack * priority_heap, Var * var)
{
  int cur_pos = var->priority_pos;

  assert (cur_pos >= 0);
  assert ((unsigned int) cur_pos < count_stack (priority_heap));
  assert (var == priority_heap->elems[cur_pos]);

  down_heap (priority_heap, cur_pos);
}


static int
update_key (Stack * priority_heap, Var * var, int old_score)
{
  int result;

  int score = var->exp_costs.score;

  if (score == old_score)
    result = 0;
  else if (score < old_score)
    {
      decrease_key (priority_heap, var);
      result = -1;
    }
  else
    {
      increase_key (priority_heap, var);
      result = 1;
    }

#ifndef NDEBUG
#if ASSERT_PRIORITY_QUEUE_HEAP_CONDITION
  if (result)
    assert_priority_queue_heap_condition (priority_heap);
#endif
#endif

  return result;
}

/* ---------- END: PRIORITY QUEUE ---------- */

#define time_stamp() 0

/*
- costs of vars on stack 'vars_marked_for_update' will be updated from scratch
- NEW: collect variables from cur. scope only 
*/
void
collect_variable_for_update (Nenofex * nenofex, Var * var)
{
  if (!nenofex->cur_scope)
    return;

  assert (cost_update_marked (var));

  if (!var->collected_for_update && var->scope == *nenofex->cur_scope)
    {
      var->collected_for_update = 1;
      push_stack (nenofex->mm, nenofex->vars_marked_for_update, var);
    }
}


static void init_lca_object (Nenofex * nenofex, LCAObject * lca_object);

static void delete_node (Nenofex * nenofex, Node * node);


/*
- delete whole graph
*/
static void
free_graph (Nenofex * nenofex)
{
  assert (nenofex);
  MemManager *mm = nenofex->mm;

  if (!nenofex->graph_root)
    return;

  Stack *stack = create_stack (mm, DEFAULT_STACK_SIZE);
  push_stack (mm, stack, nenofex->graph_root);

  Node *cur;
  while ((cur = pop_stack (stack)))
    {
      if (!is_literal_node (cur))
        {
          Node *ch;
          for (ch = cur->child_list.last; ch; ch = ch->level_link.prev)
            {
              push_stack (mm, stack, ch);
            }
        }

      if (cur->lca_child_list_occs)
        {
          delete_stack (mm, cur->lca_child_list_occs);
          assert (cur->pos_in_lca_children);
          delete_stack (mm, cur->pos_in_lca_children);
        }

      mem_free (mm, cur, sizeof (Node));
    }                           /* end: while stack not empty */

  delete_stack (mm, stack);
}


static void free_lca_children (Nenofex *nenofex, LCAObject * lca_object);


static void delete_scope (Nenofex *nenofex, Scope * scope);

/*
- create new AND-operator node
- node ID actually not relevant
*/
Node *
and_node (Nenofex * nenofex)
{
  assert (nenofex->next_free_node_id > nenofex->num_orig_vars);

#if COMPUTE_NUM_TOTAL_CREATED_NODES
  nenofex->stats.num_total_created_nodes++;
#endif

  size_t num_bytes = sizeof (Node);
  Node *result = mem_malloc (nenofex->mm, num_bytes);
  assert (result);
  memset (result, 0, num_bytes);

  result->type = NODE_TYPE_AND;
  result->id = nenofex->next_free_node_id++;

  return result;
}


/*
- create new OR-operator node
- node ID actually not relevant
*/
Node *
or_node (Nenofex * nenofex)
{
  assert (nenofex->next_free_node_id > nenofex->num_orig_vars);

#if COMPUTE_NUM_TOTAL_CREATED_NODES
  nenofex->stats.num_total_created_nodes++;
#endif

  size_t num_bytes = sizeof (Node);
  Node *result = mem_malloc (nenofex->mm, num_bytes);
  assert (result);
  memset (result, 0, num_bytes);

  result->type = NODE_TYPE_OR;
  result->id = nenofex->next_free_node_id++;

  return result;
}


/*
- create new literal node
- assign node ID actually with respect to variable and negation
*/
static Node *
lit_node (Nenofex * nenofex, int lit, Var * var)
{
  assert (lit);

#if COMPUTE_NUM_TOTAL_CREATED_NODES
  nenofex->stats.num_total_created_nodes++;
#endif

  size_t num_bytes = sizeof (Node);
  Node *result = (Node *) mem_malloc (nenofex->mm, num_bytes);
  assert (result);
  memset (result, 0, num_bytes);

  result->id = lit;
  result->type = NODE_TYPE_LITERAL;
  assert (var->id);
  assert (var->lits[0].var);
  assert (var->lits[1].var);
  result->lit = (lit < 0 ? &(var->lits[0]) : &(var->lits[1]));

  return result;
}


/*
- collect possible unates incrementally whenever one occ. list becomes empty
*/
static void
collect_variable_as_unate (Nenofex * nenofex, Var * var)
{
  if (!var->collected_as_unate)
    {
      var->collected_as_unate = 1;
      push_stack (nenofex->mm, nenofex->unates, var);
    }
}


/*
- set up new variable
- TO BE CHANGED: variables are collected twice (in scope and on separate stack)
- push all new vars on unate-stack; afterwards unates are detected incrementally
*/
static void
init_variable (Nenofex * nenofex, unsigned int abs_lit, Scope * scope)
{
  assert (abs_lit);
  assert (!(nenofex->vars[abs_lit]));

  Var *var = (Var *) mem_malloc (nenofex->mm, sizeof (Var));
  assert (var);
  memset (var, 0, sizeof (Var));

  var->exp_costs.score = INT_MIN;

  var->pos_in_lca_child_list_occs = create_stack (nenofex->mm, DEFAULT_STACK_SIZE);

  init_lca_object (nenofex, &(var->exp_costs.lca_object));

  nenofex->vars[abs_lit] = var;

  var->id = abs_lit;
  var->priority_pos = -1;
  var->lits[0].var = var;
  var->lits[0].negated = 1;
  var->lits[1].var = var;
  var->lits[1].negated = 0;
  var->lits[0].occ_list.first = (Node *) 0;
  var->lits[0].occ_list.last = (Node *) 0;
  var->lits[1].occ_list.first = (Node *) 0;
  var->lits[1].occ_list.last = (Node *) 0;

  if (!scope)                   /* add variable to default scope */
    {
      scope = nenofex->scopes->elems[0];
      assert (scope->nesting == DEFAULT_SCOPE_NESTING);
    }
  push_stack (nenofex->mm, scope->vars, var);
  scope->remaining_var_cnt++;

  /* NEW */
  add_fast_priority_queue (nenofex->mm, scope->priority_heap, var);

  var->scope = scope;

  collect_variable_as_unate (nenofex, var);

  assert (!(nenofex->vars[abs_lit]->lits[0].occ_list.first));
  assert (!(nenofex->vars[abs_lit]->lits[1].occ_list.first));
  assert (!(nenofex->vars[abs_lit]->lits[0].occ_list.last));
  assert (!(nenofex->vars[abs_lit]->lits[1].occ_list.last));
}


#ifndef NDEBUG

/*
- for assertion checking only
*/
static void
assert_occ_list_integrity (Nenofex * nenofex, Lit * lit)
{
  Node *node, *prev;
  prev = 0;
  for (node = lit->occ_list.first; node; node = node->occ_link.next)
    {
      assert (node->lit == lit);
      assert (node->num_children == 0);
      assert (node->size_subformula == 1);
      assert (is_literal_node (node));

      assert (!node->child_list.first);
      assert (!node->child_list.last);

      assert (nenofex->cur_expanded_var || !node->mark2);
      assert (nenofex->cur_expanded_var || !node->mark2);

      assert (node->id);
      assert (node->id == (lit->negated ? -lit->var->id : lit->var->id));
      assert (!prev || node->occ_link.prev == prev);
      assert (!prev || prev->occ_link.next == node);
      assert (node != lit->occ_list.first || !node->occ_link.prev);
      assert (node != lit->occ_list.last || !node->occ_link.next);
      prev = node;
    }
}


/*
- for assertion checking only
*/
static void
assert_all_occ_lists_integrity (Nenofex * nenofex)
{
  void **v_scope, **scope_end;
  scope_end = nenofex->scopes->top;

  for (v_scope = nenofex->scopes->elems; v_scope < scope_end; v_scope++)
    {
      Scope *scope = *v_scope;

      void **v_var, **var_end;
      var_end = scope->vars->top;

      for (v_var = scope->vars->elems; v_var < var_end; v_var++)
        {
          Var *var = *v_var;

          assert (var->id);
          assert (var->scope);
          assert (!var->simp_mark);

          assert (nenofex->atpg_rr_called || !var->atpg_mark);
          assert (nenofex->atpg_rr_called || !var->assignment);

          assert_occ_list_integrity (nenofex, &(var->lits[0]));
          assert_occ_list_integrity (nenofex, &(var->lits[1]));
        }                       /* end: for all scope vars */

    }                           /* end: for all scopes */
}


#ifndef NDEBUG
static unsigned int count_children (Nenofex * nenofex, Node * node);
#endif


/*
- for assertion checking only
*/
static void
assert_child_occ_list_integrity (Nenofex * nenofex, Node * parent)
{
  assert (parent->num_children == count_children (nenofex, parent));

  assert (parent != nenofex->graph_root || !parent->parent);
  assert (parent->parent || parent == nenofex->graph_root);

  /* atpg_info-pointers expected to be cleared properly */
  assert (nenofex->cur_expanded_var || !parent->atpg_info);
  assert (nenofex->cur_expanded_var || !parent->mark1);

  assert (!parent->mark2);

  if (is_literal_node (parent))
    {
      assert (!parent->child_list.first);
      assert (!parent->child_list.last);
      assert (parent->lit);
      assert (!parent->lit->var->simp_mark);
      assert (parent->id);
      assert (parent->lit->negated || parent->id > 0);
      assert (!parent->lit->negated || parent->id < 0);
      assert (parent->id == (parent->lit->negated ?
                             -parent->lit->var->id : parent->lit->var->id));

      assert (parent->lit->occ_list.first);
      assert (parent->lit->occ_list.last);
      assert (parent->occ_link.next || parent->lit->occ_list.last == parent);
      assert (parent->occ_link.prev || parent->lit->occ_list.first == parent);
    }
  else
    {
      assert (parent->id > 0);
      assert (!parent->lit);
      assert (!parent->occ_link.next);
      assert (!parent->occ_link.prev);
      assert ((unsigned int) parent->id > nenofex->num_orig_vars);
      assert (is_or_node (parent) || is_and_node (parent));

      if (!parent->child_list.first)
        {
          assert (!parent->child_list.last);
          assert (0);
        }
      else
        {
          assert (parent->child_list.last);
          assert (parent->child_list.first != parent->child_list.last);

          int op_ch_found = 0;
          Node *ch, *prev;
          prev = 0;
          for (ch = parent->child_list.first; ch; ch = ch->level_link.next)
            {
              op_ch_found = (op_ch_found || !is_literal_node (ch));

              assert (!op_ch_found || !is_literal_node (ch));

              /* atpg_info->pointers expected to be cleared properly */
              assert (nenofex->cur_expanded_var || !ch->atpg_info);
              assert (nenofex->cur_expanded_var || !ch->mark1);

              assert (!prev || ch->level_link.prev == prev);
              assert (!prev || prev->level_link.next == ch);
              assert (ch->parent->type != ch->type);
              assert (ch->parent == parent);
              assert (ch->level == parent->level + 1);
              assert (ch != parent->child_list.first || !ch->level_link.prev);
              assert (ch != parent->child_list.last || !ch->level_link.next);
              prev = ch;
            }
        }
    }                           /* end: op node */
}


/*
- for assertion checking only
*/
static void
assert_all_child_occ_lists_integrity (Nenofex * nenofex)
{
  Stack *stack = create_stack (nenofex->mm, DEFAULT_STACK_SIZE);
  push_stack (nenofex->mm, stack, nenofex->graph_root);

  Node *cur;
  while ((cur = pop_stack (stack)))
    {
      assert_child_occ_list_integrity (nenofex, cur);
      if (!is_literal_node (cur))
        {
          Node *child;
          for (child = cur->child_list.last; child;
               child = child->level_link.prev)
            {
              push_stack (nenofex->mm, stack, child);
            }
        }
    }                           /* end: while stack not empty */

  delete_stack (nenofex->mm, stack);
}


/*
- for assertion checking only
*/
static Node *
find_node_by_id (Nenofex *nenofex, Node * root, int id)
{
  Stack *stack = create_stack (nenofex->mm, 16);
  Node *cur = 0;
  push_stack (nenofex->mm, stack, (void *) root);
  while ((cur = (Node *) pop_stack (stack)))
    {
      if (cur->id == id)
        break;
      if (!is_literal_node (cur))
        {
          Node *child;
          for (child = cur->child_list.last; child;
               child = child->level_link.prev)
            push_stack (nenofex->mm, stack, (void *) child);
        }
    }                           /* end: while */
  delete_stack (nenofex->mm, stack);
  return cur;
}


/*
- for assertion checking only
*/
static Node *
find_node_by_address (Nenofex *nenofex, Node * root, Node * node)
{
  Stack *stack = create_stack (nenofex->mm, 16);
  Node *cur = 0;
  push_stack (nenofex->mm, stack, (void *) root);
  while ((cur = (Node *) pop_stack (stack)))
    {
      if (cur == node)
        break;
      if (!is_literal_node (cur))
        {
          Node *child;
          for (child = cur->child_list.last; child;
               child = child->level_link.prev)
            push_stack (nenofex->mm, stack, (void *) child);
        }
    }                           /* end: while */
  delete_stack (nenofex->mm, stack);
  return cur;
}

#endif /* end: ifndef NDEBUG */


void remove_and_free_subformula (Nenofex * nenofex, Node * root);


/* 
- simplification by inspection of child-list of a node
- will remove double literals or delete node if has two complementary literals
- called whenever a node 'root' gets a new literal-child
- INVARIANT: lits are stored first in child-list -> abort search at first op-child
- TODO: need no stack for marked nodes any more when lits are stored first in ch-list
*/
void
simplify_one_level (Nenofex * nenofex, Node * root)
{
  assert (!is_literal_node (root));

  if (root == nenofex->graph_root && is_and_node (root))
    {
      /* in this case need not check literal-children at graph root (AND) 
         except within redundancy removal and global flow */
      if (!nenofex->atpg_rr_called)
        return;
    }

#ifndef NDEBUG
#if ASSERT_SIMP_ONE_LEVEL_BEFORE
  assert_all_occ_lists_integrity (nenofex);
#endif
#endif

  Node *del_node = 0;
  Stack *marked = create_stack (nenofex->mm, DEFAULT_STACK_SIZE);

  Node *ch, *next;
  for (ch = root->child_list.first; ch && (is_literal_node (ch)); ch = next)
    {
      next = ch->level_link.next;

      Lit *lit = ch->lit;
      assert (lit);
      Var *var = lit->var;
      assert (var);

      /* BUG-FIX: must NOT simplify lits from var which is currently being expanded */
      if (var == nenofex->cur_expanded_var)
        continue;

      if (!simplify_var_marked (var))
        {
          if (lit->negated)
            simplify_var_neg_mark (var);
          else
            simplify_var_pos_mark (var);

          push_stack (nenofex->mm, marked, var);
        }
      else if (simplify_var_pos_marked (var))
        {
          if (lit->negated)     /* remove parent */
            {
              del_node = root;
              break;
            }
          else                  /* remove literal */
            {
              if (root->num_children == 2)      /* 'root' has to be merged after deletion */
                {
                  del_node = ch;
                  break;
                }
              else              /* can remove immediately */
                {
                  remove_and_free_subformula (nenofex, ch);
                }
            }
        }
      else
        {
          assert (simplify_var_neg_marked (var));

          if (lit->negated)     /* remove literal */
            {
              if (root->num_children == 2)      /* 'root' has to be merged after deletion */
                {
                  del_node = ch;
                  break;
                }
              else              /* can remove immediately */
                {
                  remove_and_free_subformula (nenofex, ch);
                }
            }
          else                  /* remove parent */
            {
              del_node = root;
              break;
            }
        }
    }                           /* end: for all children */

  /* unmark variables */
  Var **var, **start;
  start = (Var **) marked->elems;
  for (var = (Var **) marked->top - 1; var >= start; var--)
    {
      assert (simplify_var_marked (*var));
      simplify_var_unmark (*var);
    }

  if (del_node)
    {
      if (del_node == nenofex->graph_root)
        {
          if (is_and_node (del_node))
            nenofex->result = NENOFEX_RESULT_UNSAT;
          else
            nenofex->result = NENOFEX_RESULT_SAT;
        }
      remove_and_free_subformula (nenofex, del_node);
    }

#ifndef NDEBUG
#if ASSERT_SIMP_ONE_LEVEL_AFTER
  assert_all_occ_lists_integrity (nenofex);
#endif
#endif

  delete_stack (nenofex->mm, marked);
}


/* 
- prints list of nodes and their children as encountered in DFS
- mainly for debugging purposes
*/
static void
print_graph_by_traversal (Nenofex *nenofex, Node * root)
{
  Stack *stack = create_stack (nenofex->mm, 1);
  push_stack (nenofex->mm, stack, root);

  Node *cur;
  while ((cur = (Node *) pop_stack (stack)))
    {
      if (!is_literal_node (cur))
        {
          printf ("%d (%s): ", cur->id, is_or_node (cur) ? "||" : "&&");

          unsigned int old_cnt = count_stack (stack);

          Node *child;
          for (child = cur->child_list.last; child;
               child = child->level_link.prev)
            {
              push_stack (nenofex->mm, stack, (void *) child);
              assert (*(stack->top - 1) == child);
            }

          void **print_ch;
          void **old_top_p = stack->elems + old_cnt;

          assert (old_top_p < stack->top - 1);

          for (print_ch = stack->top /*_p*/  - 1; print_ch >= old_top_p;
               print_ch--)
            {
              printf ("%d", ((Node *) * print_ch)->id);
              if (is_literal_node (((Node *) * print_ch)))
                printf ("L");
              if (((Node *) * print_ch)->level_link.next)
                printf (", ");
            }
          printf ("\n");
        }
    }                           /* end: while */

  delete_stack (nenofex->mm, stack);
}


/* 
- unlink a literal from occurrence list
- same code as for unlinking from child-list, but now working on occ_links
*/
static void
unlink_node_from_occ_list (Nenofex * nenofex, Node * node)
{
  assert (node);
  assert (node->lit);
  assert (is_literal_node (node));

  if (node->occ_link.prev)
    {
      node->occ_link.prev->occ_link.next = node->occ_link.next;

      if (node->occ_link.next)
        node->occ_link.next->occ_link.prev = node->occ_link.prev;
      else
        {                       /* node == last */
          assert (node == node->lit->occ_list.last);

          node->lit->occ_list.last = node->occ_link.prev;

          assert (!node->lit->occ_list.last->occ_link.next);
        }
    }
  else
    {                           /* node == first */
      assert (node == node->lit->occ_list.first);

      node->lit->occ_list.first = node->occ_link.next;

      if (node->occ_link.next)
        {
          node->occ_link.next->occ_link.prev = node->occ_link.prev;

          assert (!node->lit->occ_list.first->occ_link.prev);
        }
      else
        {                       /* node == first == last */
          assert (node == node->lit->occ_list.last);

          node->lit->occ_list.last = node->lit->occ_list.first;

          assert (!node->lit->occ_list.first);
          assert (!node->lit->occ_list.last);
        }
    }

  node->occ_link.next = node->occ_link.prev = 0;

  assert (node->lit->occ_cnt);

  node->lit->occ_cnt--;

  if (node->lit->occ_cnt == 0)
    {
      collect_variable_as_unate (nenofex, node->lit->var);
    }
#ifndef NDEBUG
  else if (node->lit->occ_cnt == 1)
    {
      assert (node->lit->occ_list.first);
      assert (node->lit->occ_list.first == node->lit->occ_list.last);
    }
  else
    {
      assert (node->lit->occ_list.first);
      assert (node->lit->occ_list.first != node->lit->occ_list.last);
    }
#endif
}


/* 
- unlink node from child-list
*/
void
unlink_node (Nenofex * nenofex, Node * node)
{
  assert (node);

  if (!node->parent)
    {                           /* should NOT be called on graph_root */
      assert (node == nenofex->graph_root);
      assert (0);
    }

  assert (node->parent);
  assert (node->parent->child_list.first);
  assert (node->parent->child_list.last);

  if (node->level_link.prev)
    {
      node->level_link.prev->level_link.next = node->level_link.next;

      if (node->level_link.next)
        node->level_link.next->level_link.prev = node->level_link.prev;
      else
        {                       /* node == last */
          assert (node == node->parent->child_list.last);

          node->parent->child_list.last = node->level_link.prev;

          assert (!node->parent->child_list.last->level_link.next);
        }
    }
  else
    {                           /* node == first */
      assert (node == node->parent->child_list.first);

      node->parent->child_list.first = node->level_link.next;

      if (node->level_link.next)
        {
          node->level_link.next->level_link.prev = node->level_link.prev;

          assert (!node->parent->child_list.first->level_link.prev);
        }
      else
        {                       /* node == first == last */

          assert (node == node->parent->child_list.last);

          node->parent->child_list.last = node->parent->child_list.first;

          assert (!node->parent->child_list.first);
          assert (!node->parent->child_list.last);
        }
    }

  node->parent->num_children--;
  node->parent = node->level_link.next = node->level_link.prev = 0;
}


/* 
- after parent-merging: subtracts 'delta' from level of all nodes under 'root'
*/
static void
merge_parent_update_level (Nenofex *nenofex, Node * root, unsigned const int delta)
{
  assert (!is_literal_node (root));
  assert (delta == 1 || delta == 2);

  Stack *stack = create_stack (nenofex->mm, DEFAULT_STACK_SIZE);
  push_stack (nenofex->mm, stack, root);

  Node *cur;
  while ((cur = pop_stack (stack)))
    {
      cur->level -= delta;

      if (!is_literal_node (cur))
        {
          Node *child;
          for (child = cur->child_list.last; child;
               child = child->level_link.prev)
            push_stack (nenofex->mm, stack, child);
        }
    }                           /* end: while */

  delete_stack (nenofex->mm, stack);
}


/* 
- starts at 'root' and goes up via parent-pointers until graph root is reached
- updates sizes of each node on path by adding 'delta' 
- called after inserting / deleting nodes from child-list of 'root'
*/
void
update_size_subformula (Nenofex * nenofex, Node * root, const int delta)
{
  assert (root);
  assert (delta);

  Node *cur = root;
  do
    {
      cur->size_subformula += delta;
      assert ((int) cur->size_subformula > 0);
    }
  while ((cur = cur->parent));
}


#if RESTRICT_ATPG_FAULT_NODE_SET
/*
- see description in header file
*/
static void
atpg_mark_nodes_for_testing_again (Nenofex * nenofex, Node * root)
{
  assert (!nenofex->atpg_rr_abort);
  assert (!nenofex->atpg_rr_reset_changed_subformula);

  unsigned int inverted_cur_mark =
    !nenofex->atpg_rr->global_atpg_test_node_mark;
  Stack *stack = create_stack (nenofex->mm, DEFAULT_STACK_SIZE);

  if (root == nenofex->changed_subformula.lca)
    {
      if (!node_taken_from_fault_queue (root))
        root->atpg_info->next_atpg_test_node_mark = inverted_cur_mark;
      else
        root->atpg_info->cur_atpg_test_node_mark = inverted_cur_mark;

      Node **ch, *child;
      for (ch = nenofex->changed_subformula.children; (child = *ch); ch++)
        push_stack (nenofex->mm, stack, child);
    }
  else
    push_stack (nenofex->mm, stack, root);

  Node *cur;
  while ((cur = pop_stack (stack)))
    {
      if (!node_taken_from_fault_queue (cur))
        cur->atpg_info->next_atpg_test_node_mark = inverted_cur_mark;
      else
        cur->atpg_info->cur_atpg_test_node_mark = inverted_cur_mark;

      if (!is_literal_node (cur))
        {
          Node *child;
          for (child = cur->child_list.last; child;
               child = child->level_link.prev)
            push_stack (nenofex->mm, stack, child);
        }
    }                           /* end: while stack not empty */

  delete_stack (nenofex->mm, stack);
}

#endif /* end if RESTRICT_ATPG_FAULT_NODE_SET */


static void unlink_variable_from_lca_list (Var * var);


static void
reset_lca_object (Nenofex * nenofex, Var * var, LCAObject * lca_object,
                  unsigned const int clean_up_lca_child_list_occs);


/*
- if node is deleted which is LCA of at least one var -> var-list must be cleared
- variables are marked for update
*/
static void
delete_lca_reset_and_mark_variables (Nenofex * nenofex, Node * var_lca)
{
  assert (var_lca->var_lca_list.first);

  Var *var, *next;
  for (var = var_lca->var_lca_list.first; var; var = next)
    {
      next = var->same_lca_link.next;
      unlink_variable_from_lca_list (var);
      reset_lca_object (nenofex, var, &var->exp_costs.lca_object, 1);
      /* NOTE: in this case, can we fully clean lca-child-list-occs? */

      lca_update_mark (var);
      inc_score_update_mark (var);
      dec_score_update_mark (var);
      collect_variable_for_update (nenofex, var);
    }                           /* end: for all variables for which 'parent' is lca */
}


/*
- TODO: clarify failed assertions
- no problems encountered so far...
*/
static void
delete_node_remove_from_lca_child_lists (Nenofex * nenofex, Node * parent,
                                         Node * node)
{
  assert (parent->var_lca_list.first);
  assert (node);

  Stack *occs = node->lca_child_list_occs;
  /*FAILED, but can happen   --assert(lca_child_list_occs); */

  /* NOTE: above assertion failed because during relinking 
     nodes in expansion, we do NOT clean up var-entries... */

  if (!occs)
    return;                     /* BUG FIX */

  /* FAILED; happens if stack has been cleaned up before .g. during unates-elim.   
     --assert(count_stack(lca_child_list_occs)); */

  void **v_var;
#if !DELETE_EMPTY_STACKS_IN_NODES
  for (v_var = occs->elems; v_var != occs->top;)
#else
  for (v_var = occs->elems;
       (occs = node->lca_child_list_occs) && v_var != occs->top;)
#endif
    {                           /* function 'reset_lca_object' will move 'top' towards 'elems' */
      Var *var = *v_var;

      unlink_variable_from_lca_list (var);
      reset_lca_object (nenofex, var, &var->exp_costs.lca_object, 1);

      lca_update_mark (var);
      inc_score_update_mark (var);
      dec_score_update_mark (var);
      collect_variable_for_update (nenofex, var);
    }                           /* end: for all vars where 'node' occurs in LCA-child-list */

#if DELETE_EMPTY_STACKS_IN_NODES
  assert (!node->lca_child_list_occs);
  assert (!node->pos_in_lca_children);
#endif
}


static void
replace_changed_lca_child (Nenofex * nenofex, Node * old_node,
                           Node * new_node);


static void remove_changed_lca_child (Nenofex * nenofex, Node * node);


#ifndef NDEBUG
static void assert_pos_in_changed_ch_list (Nenofex * nenofex);
#endif


static void
delete_node (Nenofex * nenofex, Node * node)
{
  Stack *occs = node->lca_child_list_occs;

  if (occs)
    {
      /* start: same code as in 'delete_node_remove_from_lca_child_list' */
      void **v_var;
#if !DELETE_EMPTY_STACKS_IN_NODES
      for (v_var = occs->elems; v_var != occs->top;)
#else
      for (v_var = occs->elems;
           (occs = node->lca_child_list_occs) && v_var != occs->top;)
#endif
        {                       /* function 'reset_lca_object' will move 'top' towards 'elems' */
          Var *var = *v_var;

          unlink_variable_from_lca_list (var);
          reset_lca_object (nenofex, var, &var->exp_costs.lca_object, 1);

          lca_update_mark (var);
          inc_score_update_mark (var);
          dec_score_update_mark (var);
          collect_variable_for_update (nenofex, var);
        }                       /* end: for all vars where 'node' occurs in LCA-child-list */
      /* end: same code */

#if !DELETE_EMPTY_STACKS_IN_NODES
      delete_stack (occs);
      assert (node->pos_in_lca_children);
      delete_stack (node->pos_in_lca_children);
#else
      assert (!node->lca_child_list_occs);
      assert (!node->pos_in_lca_children);
#endif
    }
  else
    {
      assert (!node->pos_in_lca_children);
    }

  mem_free (nenofex->mm, node, sizeof (Node));
}


/* 
- typically called after deleting a node from parent's children
- parent has only one child left
- the one remaining child is linked to its grand-parent
- if remaining child is op-node -> link its children to grand-parent
- several graph properties and data structures must be maintain
- TODO: refinements (introduce variables, ...)
*/
void
merge_parent (Nenofex * nenofex, Node * parent)
{
  assert (parent);
  assert (!is_literal_node (parent));
  assert (parent->child_list.first == parent->child_list.last);
  assert (!parent->child_list.first->level_link.prev);
  assert (!parent->child_list.first->level_link.next);

#if RESTRICT_ATPG_FAULT_NODE_SET
  unsigned int mark_nodes_for_testing_again = 0;
#endif

  LCAObject *changed_subformula = &(nenofex->changed_subformula);

  if (!parent->parent)
    {                           /* 'graph-root' to be set */
      assert (parent == nenofex->graph_root);
      assert (!parent->level_link.next);
      assert (!parent->level_link.prev);

      if (parent->atpg_info)
        mark_fault_node_as_deleted (parent->atpg_info->fault_node);

      if (parent == changed_subformula->lca &&
          !nenofex->atpg_rr_reset_changed_subformula)
        {

          if (nenofex->atpg_rr_called)
            {
              nenofex->atpg_rr_abort = 1;
            }

          assert (changed_subformula->num_children == 2);
          reset_changed_lca_object (nenofex);

          /* if 'changed' would become a single literal, then do nothing */

          if (!is_literal_node (parent->child_list.first))
            {
              nenofex->atpg_rr_abort = 0;

              changed_subformula->lca = parent->child_list.first;

              Node *child;
              for (child = changed_subformula->lca->child_list.first;
                   child; child = child->level_link.next)
                add_changed_lca_child (nenofex, child);

#ifndef NDEBUG
#if ASSERT_POS_IN_CHANGED_CH_LIST
              assert_pos_in_changed_ch_list (nenofex);
#endif
#endif
              assert (changed_subformula->num_children >= 2);
              assert (changed_subformula->top_p ==
                      changed_subformula->children +
                      changed_subformula->num_children);
            }                   /* end: new lca is op-node */

        }                       /* end: parent is lca of 'changed_subformula' */
      else if (parent == changed_subformula->lca)
        {
          assert (nenofex->atpg_rr_abort);
          assert (nenofex->atpg_rr_called);
          nenofex->atpg_rr_reset_changed_subformula = 0;
          reset_changed_lca_object (nenofex);
        }

      nenofex->graph_root = parent->child_list.first;
      assert (nenofex->graph_root->parent);
      nenofex->graph_root->parent = 0;

      if (!is_literal_node (parent->child_list.first))
        merge_parent_update_level (nenofex, parent->child_list.first, 1);
      else
        nenofex->graph_root->level = 0;

      if (parent->var_lca_list.first)
        {
          assert (parent->var_lca_list.last);
          delete_lca_reset_and_mark_variables (nenofex, parent);
        }

#if COMPUTE_NUM_DELETED_NODES
      nenofex->stats.total_deleted_nodes++;
      if (nenofex->atpg_rr_called)
        nenofex->stats.deleted_nodes_by_global_flow_redundancy++;
#endif

      delete_node (nenofex, parent);
      return;
    }

  /* grandparent has more than one child */
  assert (parent->parent->child_list.first !=
          parent->parent->child_list.last);

  /* unlink remaining child (or its children) and add to grandparent's ch-list */
  Node *sub_parent = parent->child_list.first;
  unlink_node (nenofex, parent->child_list.first);

  assert (!parent->child_list.first);
  assert (!parent->child_list.last);

  unsigned int lit_copied = 0;
  if (is_literal_node (sub_parent))
    {
#if RESTRICT_ATPG_FAULT_NODE_SET
      mark_nodes_for_testing_again = 1;
#endif

      /* 'sub_parent' is either lit in cur. subformula or 
         directly linked to node on path up to root */
      Var *var = sub_parent->lit->var;

      if (var->exp_costs.lca_object.lca)        /* BUG FIX */
        {
          dec_score_update_mark (var);
          collect_variable_for_update (nenofex, var);
        }

      /* since 'sub_parent' is literal, do not set new 'changed' */

      if (parent == changed_subformula->lca)
        {
          if (!nenofex->atpg_rr_reset_changed_subformula)
            {
              assert (changed_subformula->num_children == 2);
              reset_changed_lca_object (nenofex);

              if (nenofex->atpg_rr_called)
                nenofex->atpg_rr_abort = 1;
            }
          else
            {
              assert (nenofex->atpg_rr_abort);
              assert (nenofex->atpg_rr_called);
              changed_subformula->lca = parent->parent; /* move LCA in order to mark vars later */
            }
        }
      else if (parent->parent == changed_subformula->lca)
        {                       /* remove 'parent', add 'sub_parent' to changed-child list */
          assert (!nenofex->atpg_rr_reset_changed_subformula);

          replace_changed_lca_child (nenofex, parent, sub_parent);

#ifndef NDEBUG
#if ASSERT_POS_IN_CHANGED_CH_LIST
          assert_pos_in_changed_ch_list (nenofex);
#endif
#endif
          assert (changed_subformula->num_children >= 2);
          assert (changed_subformula->top_p ==
                  changed_subformula->children +
                  changed_subformula->num_children);
        }
      else if (sub_parent == changed_subformula->lca)
        assert (0);             /* sub_parent is literal -> not allowed */

      add_node_to_child_list (nenofex, parent->parent, sub_parent);     /* sets level */
      assert (sub_parent->occ_link.next ||
              sub_parent->occ_link.prev
              || sub_parent == sub_parent->lit->occ_list.first);

      lit_copied = 1;

      if (parent->atpg_info)
        {
          assert (nenofex->atpg_rr_called);
          mark_fault_node_as_deleted (parent->atpg_info->fault_node);

          if (parent->parent->atpg_info && parent->parent->atpg_info->atpg_ch)
            push_stack (nenofex->mm, parent->parent->atpg_info->atpg_ch,
                        sub_parent->atpg_info->fault_node);
        }
    }
  else                          /* sub_parent is operator node */
    {
      /* NOTE: simplify checks by setting LCA to parent->parent first in all cases? */

      if (sub_parent == changed_subformula->lca)
        {                       /* sub_parent's children remain in child list, need to set new LCA 
                                   since children are copied up to grand-parent */
          assert (!nenofex->atpg_rr_reset_changed_subformula);

          if (nenofex->atpg_rr_called)
            nenofex->atpg_rr_abort = 1;
        }
      if (parent == changed_subformula->lca)
        {                       /* relink sub_parent's children */
          if (!nenofex->atpg_rr_reset_changed_subformula)
            {
              assert (changed_subformula->num_children == 2);
              reset_changed_lca_object (nenofex);
              changed_subformula->lca = parent; /* workaround - set flag for relinking */

              if (nenofex->atpg_rr_called)
                nenofex->atpg_rr_abort = 1;
            }
          else
            {
              assert (nenofex->atpg_rr_called);
              assert (nenofex->atpg_rr_abort);
              changed_subformula->lca = parent->parent;
            }
        }
      else if (parent->parent == changed_subformula->lca)
        {                       /* relink sub_parent's children */
          assert (!nenofex->atpg_rr_reset_changed_subformula);
          remove_changed_lca_child (nenofex, parent);
        }

      if (parent->atpg_info)
        {
          assert (nenofex->atpg_rr_called);
          mark_fault_node_as_deleted (parent->atpg_info->fault_node);
        }

      if (sub_parent->atpg_info)
        {
          assert (nenofex->atpg_rr_called);
          mark_fault_node_as_deleted (sub_parent->atpg_info->fault_node);
        }

      assert (sub_parent->type == parent->parent->type);
      assert (sub_parent->child_list.first != sub_parent->child_list.last);

      Node *child, *next;
      for (child = sub_parent->child_list.first; child; child = next)
        {
          next = child->level_link.next;

          if (!is_literal_node (child))
            merge_parent_update_level (nenofex, child, 2);

          unlink_node (nenofex, child);
          add_node_to_child_list (nenofex, parent->parent, child);      /* levels are set */

          /* TODO: can handle literals early */
          if (is_literal_node (child))
            {
              assert (child->occ_link.next ||
                      child->occ_link.prev
                      || child == child->lit->occ_list.first);
              lit_copied = 1;

#if RESTRICT_ATPG_FAULT_NODE_SET
              mark_nodes_for_testing_again = 1;
#endif

              /* 'child' is either lit in cur. subformula (then var is already dec-score-marked)
                 or linked to node which is linked to path up to root */
              Var *var = child->lit->var;
              if (var->exp_costs.lca_object.lca)        /* BUG FIX */
                {
                  dec_score_update_mark (var);
                  collect_variable_for_update (nenofex, var);
                }
            }                   /* end: is literal */

#ifndef NDEBUG
          if (parent->parent->atpg_info)
            assert (nenofex->atpg_rr_called);
#endif

          /* push children on watcher stack */
          if (parent->parent->atpg_info && parent->parent->atpg_info->atpg_ch)
            push_stack (nenofex->mm, parent->parent->atpg_info->atpg_ch,
                        child->atpg_info->fault_node);

          /* NOTE: simplify check by setting lca to parent->parent first in all cases ? */
          if (!nenofex->atpg_rr_reset_changed_subformula &&
              (parent == changed_subformula->lca
               || parent->parent == changed_subformula->lca))
            add_changed_lca_child (nenofex, child);
        }                       /* end: for all children */

      if (!nenofex->atpg_rr_reset_changed_subformula &&
          (sub_parent == changed_subformula->lca
           || parent == changed_subformula->lca))
        {
          changed_subformula->lca = parent->parent;
#ifndef NDEBUG
#if ASSERT_POS_IN_CHANGED_CH_LIST
          assert_pos_in_changed_ch_list (nenofex);
#endif
#endif
          assert (changed_subformula->num_children >= 2);
          assert (changed_subformula->top_p ==
                  changed_subformula->children +
                  changed_subformula->num_children);
        }

      if (sub_parent->var_lca_list.first)
        {
          assert (sub_parent->var_lca_list.last);
          delete_lca_reset_and_mark_variables (nenofex, sub_parent);
        }

#if COMPUTE_NUM_DELETED_NODES
      nenofex->stats.total_deleted_nodes++;
      if (nenofex->atpg_rr_called)
        nenofex->stats.deleted_nodes_by_global_flow_redundancy++;
#endif

      delete_node (nenofex, sub_parent);
    }                           /* end: sub_parent is operator node */

  /* unlink parent */
  Node *parent_parent = parent->parent;
  unlink_node (nenofex, parent);

  /* need to update watchers if parent->parent will not be reset afterwards */
  if (parent_parent->atpg_info)
    {
      assert (nenofex->atpg_rr_called);
      collect_assigned_node (nenofex->atpg_rr, parent_parent);

      if (parent_parent->atpg_info->atpg_ch)
        parent_parent->atpg_info->clean_up_watcher_list = 1;
    }

  if (parent->var_lca_list.first)
    {
      assert (parent->var_lca_list.last);
      delete_lca_reset_and_mark_variables (nenofex, parent);
    }


  if (parent_parent->var_lca_list.first)
    {
      assert (parent_parent->var_lca_list.last);
      delete_node_remove_from_lca_child_lists (nenofex, parent_parent,
                                               parent);
    }

#if COMPUTE_NUM_DELETED_NODES
  nenofex->stats.total_deleted_nodes++;
  if (nenofex->atpg_rr_called)
    nenofex->stats.deleted_nodes_by_global_flow_redundancy++;
#endif

  if (parent == nenofex->existential_split_or)
    nenofex->existential_split_or = 0;

  delete_node (nenofex, parent);


#if RESTRICT_ATPG_FAULT_NODE_SET
  if (mark_nodes_for_testing_again && !nenofex->atpg_rr_abort &&
      nenofex->atpg_rr_called && !nenofex->atpg_rr->global_flow_optimizing)
    atpg_mark_nodes_for_testing_again (nenofex, parent_parent);
#endif

  assert (!nenofex->atpg_rr_reset_changed_subformula
          || nenofex->atpg_rr_abort);

  if (lit_copied)
    {
      simplify_one_level (nenofex, parent_parent);
    }

  assert (!nenofex->changed_subformula.lca ||
          !is_literal_node (nenofex->changed_subformula.lca));
}


/* 
- unlinks the subformula rooted at 'root' from its parent's child-list 
- recursively frees all nodes; merge nodes if parent has 1 child left after del.
- several properties and data structures must be maintained within this function
- TODO: refinements (introduce variables, ...)
*/
void
remove_and_free_subformula (Nenofex * nenofex, Node * root)
{
#if COMPUTE_NUM_DELETED_NODES
  nenofex->stats.total_deleted_nodes += root->size_subformula;
  if (nenofex->atpg_rr_called)
    nenofex->stats.deleted_nodes_by_global_flow_redundancy +=
      root->size_subformula;
#endif

  Node *parent = root->parent;
  LCAObject *changed_subformula = &(nenofex->changed_subformula);

  assert (!nenofex->changed_subformula.lca ||
          nenofex->changed_subformula.lca->level <= root->level);

  if (root == nenofex->changed_subformula.lca)
    {
      if (!nenofex->atpg_rr_called)
        {
          assert (!is_literal_node (root));
          reset_changed_lca_object (nenofex);
        }
      else                      /* remember root's parent for marking variables */
        {
          nenofex->atpg_rr_abort = 1;
          nenofex->atpg_rr_reset_changed_subformula = 1;
          reset_changed_lca_object (nenofex);   /* BUG FIX */
          nenofex->changed_subformula.lca = parent;
        }
    }

  /* sufficient check: no successor of 'root' can equal 'existential_split_or' */
  if (root == nenofex->existential_split_or)
    nenofex->existential_split_or = 0;

  if (!parent)
    {                           /* handle deletion of graph-root */
      assert (root == nenofex->graph_root ||
              nenofex->distributivity_deleting_redundancies);
      goto FREE_GRAPH;
    }

  unlink_node (nenofex, root);

  int update_size_delta = root->size_subformula;

  assert (parent->child_list.first);
  assert (parent->child_list.last);

  if (parent->child_list.first == parent->child_list.last)
    {
      update_size_delta++;

      if (!is_literal_node (parent->child_list.first))
        update_size_delta++;

      update_size_subformula (nenofex, parent, -update_size_delta);
      merge_parent (nenofex, parent);
    }
  else                          /*no merging necessary */
    {
      update_size_subformula (nenofex, parent, -update_size_delta);

      if (root->changed_ch_list_pos)
        {                       /* must remove 'root' from changed-child list */
          assert (parent == changed_subformula->lca);
          remove_changed_lca_child (nenofex, root);

          /* if only 1 child left -> new "changed-subformula" if it not a literal */
          if (changed_subformula->num_children == 1)
            {
              assert (*changed_subformula->children);   /* remaining child on first pos */
              assert (*(changed_subformula->children + 1) == 0);

              /* 'parent' remains in graph, but must be excluded from testing */
              if (nenofex->atpg_rr_called)
                parent->atpg_info->fault_node->skip = 1;

              Node *remaining_child = *changed_subformula->children;

              reset_changed_lca_object (nenofex);

              if (!is_literal_node (remaining_child))
                {
                  changed_subformula->lca = remaining_child;
                  Node *ch;
                  for (ch = remaining_child->child_list.first; ch;
                       ch = ch->level_link.next)
                    add_changed_lca_child (nenofex, ch);

#ifndef NDEBUG
#if ASSERT_POS_IN_CHANGED_CH_LIST
                  assert_pos_in_changed_ch_list (nenofex);
#endif
#endif
                  assert (changed_subformula->num_children >= 2);
                  assert (changed_subformula->top_p ==
                          changed_subformula->children +
                          changed_subformula->num_children);
                }
              else if (nenofex->atpg_rr_called)
                {
                  nenofex->atpg_rr_abort = 1;
                  changed_subformula->lca = parent;
                  nenofex->atpg_rr_reset_changed_subformula = 1;
                }

            }                   /* end: only one child remaining */
        }                       /* end: 'root' is child of 'changed-subformula' */

      if (parent->var_lca_list.first)
        {                       /* 'root' possibly occurs in lca-ch list of a variable 
                                   -> must initialize such variables from scratch */
          assert (parent->var_lca_list.last);
          delete_node_remove_from_lca_child_lists (nenofex, parent, root);
        }                       /* end: parent is lca of a variable */

      /* need to update watchers if parent will not be reset afterwards */
      if (parent->atpg_info)
        {
          assert (nenofex->atpg_rr_called);
          collect_assigned_node (nenofex->atpg_rr, parent);

          if (parent->atpg_info->atpg_ch)
            parent->atpg_info->clean_up_watcher_list = 1;
        }
    }                           /* end: no merging necessary */

  if (is_literal_node (root))
    {
      unlink_node_from_occ_list (nenofex, root);

      assert (!root->occ_link.next);
      assert (!root->occ_link.prev);

      Var *var = root->lit->var;
      if (var != nenofex->cur_expanded_var)
        {
          lca_update_mark (var);
          inc_score_update_mark (var);
          dec_score_update_mark (var);
          collect_variable_for_update (nenofex, var);
        }

#ifndef NDEBUG
      if (root == changed_subformula->lca)
        assert (0);
#endif

      if (root->atpg_info)
        mark_fault_node_as_deleted (root->atpg_info->fault_node);

      if (root->var_lca_list.first)
        {                       /* CONJECTURE: should never occur if unates eliminated until saturation */
          Var *var = root->lit->var;

          assert (root->var_lca_list.first == root->var_lca_list.last);
          assert (root->var_lca_list.first == var);
          /* var has exactly one occ */
          assert (!var->lits[0].occ_list.first ||
                  var->lits[0].occ_list.first == var->lits[0].occ_list.last);
          assert (!var->lits[1].occ_list.first ||
                  var->lits[1].occ_list.first == var->lits[1].occ_list.last);
          assert (!var->lits[0].occ_list.first
                  || !var->lits[1].occ_list.first);
          assert (!var->lits[1].occ_list.first
                  || !var->lits[0].occ_list.first);

          unlink_variable_from_lca_list (var);
          reset_lca_object (nenofex, var,
                            &root->lit->var->exp_costs.lca_object, 1);
        }

      delete_node (nenofex, root);
      return;
    }                           /* end: root is literal */

FREE_GRAPH:;

  Stack *stack = create_stack (nenofex->mm, DEFAULT_STACK_SIZE);
  push_stack (nenofex->mm, stack, root);

  Node *cur;
  while ((cur = pop_stack (stack)))
    {
      if (is_literal_node (cur))
        {
          unlink_node_from_occ_list (nenofex, cur);

          Var *var = cur->lit->var;

          if (var != nenofex->cur_expanded_var)
            {
              lca_update_mark (var);
              inc_score_update_mark (var);
              dec_score_update_mark (var);
              collect_variable_for_update (nenofex, var);
            }

          if (cur->atpg_info)
            mark_fault_node_as_deleted (cur->atpg_info->fault_node);

          if (cur->var_lca_list.first)
            {                   /* CONJECTURE: should never occur if unates eliminated until saturation */
              assert (cur->var_lca_list.first == cur->var_lca_list.last);
              assert (cur->var_lca_list.first == var);
              assert (var->exp_costs.lca_object.lca);

              unlink_variable_from_lca_list (var);
              reset_lca_object (nenofex, var, &var->exp_costs.lca_object, 1);
            }

          delete_node (nenofex, cur);
        }
      else                      /* 'cur' is operator node */
        {
          Node *ch;
          for (ch = cur->child_list.last; ch; ch = ch->level_link.prev)
            {
              push_stack (nenofex->mm, stack, ch);
            }

          if (cur->atpg_info)
            mark_fault_node_as_deleted (cur->atpg_info->fault_node);

          if (cur->var_lca_list.first)
            {
              assert (cur->var_lca_list.last);
              Var *var, *next;
              for (var = cur->var_lca_list.first; var; var = next)
                {
                  next = var->same_lca_link.next;
                  unlink_variable_from_lca_list (var);
                  reset_lca_object (nenofex, var, &var->exp_costs.lca_object,
                                    1);
                  /* NOTE: in this case, need NOT clean lca-child-list-occs? */
                }               /* end: for all variables for which 'parent' is lca */
            }

          delete_node (nenofex, cur);
        }                       /* end: 'cur' is operator node */
    }                           /* end: while stack not empty */
  delete_stack (nenofex->mm, stack);

  if (!parent && !nenofex->distributivity_deleting_redundancies)
    {
      nenofex->graph_root = 0;
    }

  assert (!nenofex->atpg_rr_reset_changed_subformula
          || nenofex->atpg_rr_abort);
  assert (!nenofex->changed_subformula.lca
          || !is_literal_node (nenofex->changed_subformula.lca));
}


/*
- used during LCA-computation
*/
static void
unmark_lca_children (LCAObject * lca_object)
{
  Node **lca_child, *child;
  for (lca_child = lca_object->children; (child = *lca_child); lca_child++)
    {
      if (!is_literal_node (child))
        {
          assert (lca_child_marked (child));
          unmark_lca_child (child);
        }
    }                           /* end: for */
}


#ifndef NDEBUG
/*
- for assertion checking only
*/
static void
assert_all_lca_children_unmarked (LCAObject * lca_object)
{
  Node **lca_child;
  for (lca_child = lca_object->children; *lca_child; lca_child++)
    {
      if (!is_literal_node ((*lca_child)))
        {
          assert (!lca_child_marked (*lca_child));
        }
    }
}
#endif /* end ifndef NDEBUG */


static void
init_lca_object (Nenofex *nenofex, LCAObject * lca_object)
{
  assert (LCA_CHILDREN_INIT_SIZE > 0);

  lca_object->lca = 0;
  lca_object->num_children = 0;
  lca_object->size_children = LCA_CHILDREN_INIT_SIZE;

  size_t bytes = LCA_CHILDREN_INIT_SIZE * sizeof (Node *);
  lca_object->children = (Node **) mem_malloc (nenofex->mm, bytes);
  assert (lca_object->children);
  memset (lca_object->children, 0, bytes);

  lca_object->top_p = lca_object->children;
}


static void
free_lca_children (Nenofex *nenofex, LCAObject * lca_object)
{
  mem_free (nenofex->mm, lca_object->children,
            lca_object->size_children * sizeof (Node *));
  lca_object->children = 0;
}


static void
enlarge_lca_children (Nenofex *nenofex, LCAObject * lca_object)
{
  assert (lca_object->num_children == lca_object->size_children);
  assert (lca_object->top_p ==
          (lca_object->children + lca_object->size_children));

  unsigned int old_size = lca_object->size_children;
  lca_object->size_children *= 2;

  lca_object->children =
    (Node **) mem_realloc (nenofex->mm, lca_object->children, old_size * sizeof (Node *),
                           lca_object->size_children * sizeof (Node *));
  assert (lca_object->children);
  memset (lca_object->children + old_size, 0,
          (lca_object->size_children - old_size) * sizeof (Node *));

  lca_object->top_p = lca_object->children + lca_object->num_children;

  assert (!*(lca_object->top_p));
  assert (lca_object->top_p ==
          (lca_object->children + lca_object->num_children));
}


static void
add_lca_child (Nenofex *nenofex, LCAObject * lca_object, Node * child)
{
  assert (lca_object->num_children < lca_object->size_children);
  assert (!*(lca_object->top_p));

  *(lca_object->top_p) = child;

  lca_object->num_children++;
  lca_object->top_p++;

  if (lca_object->num_children == lca_object->size_children)
    enlarge_lca_children (nenofex, lca_object);

}


static void
clear_lca_children (LCAObject * lca_object)
{
  unmark_lca_children (lca_object);
  memset (lca_object->children, 0,
          lca_object->num_children * sizeof (Node *));
  lca_object->num_children = 0;
  lca_object->top_p = lca_object->children;
}


#ifndef NDEBUG
void
assert_all_lca_occ_pos_integrity (Nenofex * nenofex)
{
  void **v_scope;
  for (v_scope = nenofex->scopes->elems; v_scope < nenofex->scopes->top;
       v_scope++)
    {
      Scope *scope = (Scope *) * v_scope;
      void **v_var;
      for (v_var = scope->vars->elems; v_var < scope->vars->top; v_var++)
        {
          Var *var = (Var *) * v_var;
          Node **ch, *child;
          unsigned long int child_pos = 0;
          for (ch = var->exp_costs.lca_object.children; (child = *ch);
               ch++, child_pos++)
            {
              unsigned long int vpos_in_occs =
                (unsigned long int) *(var->pos_in_lca_child_list_occs->elems +
                                      child_pos);
              assert (var ==
                      (Var *) * (child->lca_child_list_occs->elems +
                                 vpos_in_occs));
              assert (child_pos ==
                      (unsigned long int) *(child->pos_in_lca_children->
                                            elems + vpos_in_occs));
            }
        }
    }
}
#endif


static void
remove_lca_child_list_occ (Nenofex * nenofex, Node * child,
                           unsigned long int child_pos, Var * var)
{
  Stack *child_lca_child_list_occs = child->lca_child_list_occs;
  Stack *child_pos_in_lca_children = child->pos_in_lca_children;
#ifndef NDEBUG
  Node **var_lca_children = var->exp_costs.lca_object.children;
#endif
  Stack *var_pos_in_lca_child_list_occs = var->pos_in_lca_child_list_occs;

  assert (count_stack (child_lca_child_list_occs) &&
          count_stack (child_lca_child_list_occs) ==
          count_stack (child_pos_in_lca_children));
  assert (var->exp_costs.lca_object.num_children &&
          var->exp_costs.lca_object.num_children ==
          count_stack (var_pos_in_lca_child_list_occs));
  assert (var_pos_in_lca_child_list_occs->elems + child_pos <
          var_pos_in_lca_child_list_occs->end);

  unsigned long int var_pos = (unsigned long int)
    *(var_pos_in_lca_child_list_occs->elems + child_pos);

  assert (child_lca_child_list_occs->elems + var_pos <
          child_lca_child_list_occs->end);
  assert ((Var *) * (child_lca_child_list_occs->elems + var_pos) == var);
  assert (child_pos < var->exp_costs.lca_object.num_children);
  assert (*(var_lca_children + child_pos) == child);
  assert (child_pos_in_lca_children->elems + var_pos <
          child_pos_in_lca_children->end);
  assert ((unsigned long int)
          *(child_pos_in_lca_children->elems + var_pos) == child_pos);

  void **v_var = child_lca_child_list_occs->elems + var_pos;
  assert (v_var < child_lca_child_list_occs->top);
  assert (var == (Var *) * v_var);

  /* cut off */
  child_lca_child_list_occs->top--;
  child_pos_in_lca_children->top--;

  if (v_var != child_lca_child_list_occs->top)
    {                           /* was not last element: overwrite and restore position info */
      assert (count_stack (child_lca_child_list_occs));
      void **ch_pos_in_lca_ch_elems = child_pos_in_lca_children->elems;
      unsigned int other_var_child_pos_index =
        count_stack (child_lca_child_list_occs);
      unsigned long int other_var_child_pos =
        (unsigned long int) *(ch_pos_in_lca_ch_elems +
                              other_var_child_pos_index);

      *v_var = *child_lca_child_list_occs->top; /* overwrite by  last elems */
      *(ch_pos_in_lca_ch_elems + var_pos) =
        *(ch_pos_in_lca_ch_elems + count_stack (child_pos_in_lca_children));

      Var *other_var = *v_var;
      assert (*(other_var->exp_costs.lca_object.children +
                other_var_child_pos) == child);
      assert ((unsigned long int)
              *(other_var->pos_in_lca_child_list_occs->elems +
                other_var_child_pos) == other_var_child_pos_index);
      *(other_var->pos_in_lca_child_list_occs->elems + other_var_child_pos) =
        (void *) var_pos;
    }
#if DELETE_EMPTY_STACKS_IN_NODES
  else if (child_lca_child_list_occs->top == child_lca_child_list_occs->elems)
    {                           /* both stacks are empty -> delete */
      delete_stack (nenofex->mm, child_lca_child_list_occs);
      child->lca_child_list_occs = 0;
      delete_stack (nenofex->mm, child_pos_in_lca_children);
      child->pos_in_lca_children = 0;
    }

#endif
}


static void
reset_lca_object (Nenofex * nenofex, Var * var, LCAObject * lca_object,
                  unsigned const int clean_up_lca_child_list_occs)
{
  assert (&var->exp_costs.lca_object == lca_object);

  if (!clean_up_lca_child_list_occs)
    memset (lca_object->children, 0,
            lca_object->num_children * sizeof (Node *));
  else
    {
      unsigned long int child_pos = 0;
      Node **ch, *child;
      for (ch = lca_object->children; (child = *ch); ch++, child_pos++)
        {
          remove_lca_child_list_occ (nenofex, child, child_pos, var);
          *ch = 0;
        }                       /* end: for all LCA-children */
    }                           /* end: remove 'var' from 'lca-child-list-occs' */

  lca_object->num_children = 0;
  lca_object->top_p = lca_object->children;
  lca_object->lca = 0;

#ifndef NDEBUG
#if ASSERT_ALL_LCA_OCC_POS_INTEGRITY
  assert_all_lca_occ_pos_integrity (nenofex);
#endif
#endif
}


/* 
- find root of smallest subformula which contains both node 'a' and node 'b'
- collects root's children which contain a,b (since 'root' is n-ary)
*/
static void
find_lca_and_children (Nenofex * nenofex, Node * a, Node * b,
                       LCAObject * lca_object)
{
  assert (a || b);
  assert (!lca_object->lca || lca_object->lca == a || lca_object->lca == b);

#if COMPUTE_LCA_PARENT_VISITS
  nenofex->stats.num_total_lca_algo_calls++;
#endif

  if (!a)
    {
      lca_object->lca = b;
      return;
    }

  if (!b || a == b)
    {
      lca_object->lca = a;
      return;
    }

#ifndef NDEBUG
  if (a != b)
    {
      assert (a->parent || b->parent);
      assert (b->parent || a->parent);
    }
#endif

  Node *high_node, *low_node, *high_node_prev, *low_node_prev;

  low_node_prev = 0;

  if (a->level >= b->level)
    {
      high_node = b;
      low_node = a;
    }
  else
    {
      high_node = a;
      low_node = b;
    }

  unsigned const int high_node_level = high_node->level;

  while (high_node_level < low_node->level)
    {
#if COMPUTE_LCA_PARENT_VISITS
      nenofex->stats.num_total_lca_parent_visits++;
#endif
      low_node_prev = low_node;
      low_node = low_node->parent;
    }

  if (high_node == low_node)
    {
      if (!lca_child_marked (low_node_prev)
          && !is_literal_node (low_node_prev))
        {
          mark_lca_child (low_node_prev);
          add_lca_child (nenofex, lca_object, low_node_prev);
        }
      else if (is_literal_node (low_node_prev))
        add_lca_child (nenofex, lca_object, low_node_prev);
    }
  else
    {                           /* high != low -> move up successively in parallel */
      do
        {
#if COMPUTE_LCA_PARENT_VISITS
          nenofex->stats.num_total_lca_parent_visits += 2;
#endif
          low_node_prev = low_node;
          low_node = low_node->parent;

          high_node_prev = high_node;
          high_node = high_node->parent;

          assert (high_node);
          assert (low_node);
        }
      while (high_node != low_node);
      assert (high_node);

      /* clear and add both children */
      clear_lca_children (lca_object);

      if (!is_literal_node (low_node_prev))
        {
          assert (!lca_child_marked (low_node_prev));
          mark_lca_child (low_node_prev);
        }
      add_lca_child (nenofex, lca_object, low_node_prev);

      if (!is_literal_node (high_node_prev))
        {
          assert (!lca_child_marked (high_node_prev));
          mark_lca_child (high_node_prev);
        }
      add_lca_child (nenofex, lca_object, high_node_prev);

    }

  lca_object->lca = high_node;
}


#ifndef NDEBUG
/* 
- used in assertion checking only 
*/
static Node *
node_has_child (Node * node, Node * child)
{
  Node *cur;
  for (cur = node->child_list.first;
       cur && cur != child; cur = cur->level_link.next)
    ;
  return cur;
}


static void
assert_lca_object_integrity (Nenofex * nenofex,
                             LCAObject * lca_object, Var * var)
{
  assert (lca_object == &(var->exp_costs.lca_object));

  assert (lca_object);
  assert (lca_object->lca);

  if (is_literal_node (lca_object->lca))
    {
      assert (lca_object->num_children == 0);
      assert (lca_object->children == lca_object->top_p);
      assert (*lca_object->top_p == 0);
      return;
    }

  Node **cur_p;
  /* each collected child has to contain either pos. or neg. lit, 
     and is marked if is an OP-node */
  for (cur_p = lca_object->children; *cur_p; cur_p++)
    {
      if (!is_literal_node ((*cur_p)))
        assert (lca_child_marked (*cur_p));

      assert (node_has_child (lca_object->lca, *cur_p));
      assert (find_node_by_id (nenofex, *cur_p, var->id)
              || find_node_by_id (nenofex, *cur_p, -var->id));
    }

  Node *cur;
  /* all occs of a vars must be contained in subformula of some child of lca */
  for (cur = var->lits[0].occ_list.first; cur; cur = (cur)->occ_link.next)
    {
      Node **child, *found;
      found = 0;
      for (child = lca_object->children; *child && !found; child++)
        {
          found = find_node_by_address (nenofex, *child, cur);
        }
      assert (found);
    }
  for (cur = var->lits[1].occ_list.first; cur; cur = (cur)->occ_link.next)
    {
      Node **child, *found;
      found = 0;
      for (child = lca_object->children; *child && !found; child++)
        {
          found = find_node_by_address (nenofex, *child, cur);
        }
      assert (found);
    }

  /* each collected child occurs exactly once in list */
  unsigned int i;
  for (i = 0; lca_object->children[i]; i++)
    {
      unsigned int j;
      for (j = 0; j < i; j++)
        {
          assert (lca_object->children[i] != lca_object->children[j]);
        }
      for (j = i + 1; lca_object->children[j]; j++)
        {
          assert (lca_object->children[i] != lca_object->children[j]);
        }
    }

  assert (is_literal_node (lca_object->lca) || lca_object->num_children >= 2);
  assert (!is_literal_node (lca_object->lca)
          || lca_object->num_children == 0);
}
#endif /* end: ifndef NDEBUG */


/*
- add a variable to LCA-list of its LCA
*/
static void
add_variable_to_lca_list (Nenofex * nenofex, Var * var)
{
  Node *lca = var->exp_costs.lca_object.lca;

  assert (lca);
  /* var must have been properly unlinked before */
  assert (!var->same_lca_link.prev);
  assert (!var->same_lca_link.next);

  if (!lca->var_lca_list.first)
    {                           /* add to empty list */
      assert (!lca->var_lca_list.last);

      lca->var_lca_list.first = lca->var_lca_list.last = var;
    }
  else                          /* append */
    {
      assert (lca->var_lca_list.last);
      assert (lca->var_lca_list.first == lca->var_lca_list.last ||
              lca->var_lca_list.last->same_lca_link.prev);
      assert (lca->var_lca_list.first != lca->var_lca_list.last ||
              !lca->var_lca_list.last->same_lca_link.prev);
      assert (!lca->var_lca_list.last->same_lca_link.next);

      lca->var_lca_list.last->same_lca_link.next = var;
      var->same_lca_link.prev = lca->var_lca_list.last;
      lca->var_lca_list.last = var;
    }
}


#if 1
/*
- unlink a variable from LCA-list of its LCA
*/
static void
unlink_variable_from_lca_list (Var * var)
{
  Node *lca = var->exp_costs.lca_object.lca;

  assert (lca);
  assert (var != lca->var_lca_list.first || !var->same_lca_link.prev);
  assert (var == lca->var_lca_list.first || var->same_lca_link.prev);
  assert (var != lca->var_lca_list.last || !var->same_lca_link.next);
  assert (var == lca->var_lca_list.last || var->same_lca_link.next);

  if (var->same_lca_link.prev)
    {
      var->same_lca_link.prev->same_lca_link.next = var->same_lca_link.next;

      if (var->same_lca_link.next)
        {
          var->same_lca_link.next->same_lca_link.prev =
            var->same_lca_link.prev;
          var->same_lca_link.next = var->same_lca_link.prev = 0;
        }
      else
        {                       /* var == last */
          assert (var == lca->var_lca_list.last);

          lca->var_lca_list.last = var->same_lca_link.prev;
          var->same_lca_link.prev = 0;

          assert (!lca->var_lca_list.last->same_lca_link.next);
        }
    }
  else
    {                           /* var == first */
      assert (var == lca->var_lca_list.first);

      lca->var_lca_list.first = var->same_lca_link.next;

      if (var->same_lca_link.next)
        {
          var->same_lca_link.next->same_lca_link.prev =
            var->same_lca_link.prev;
          var->same_lca_link.next = 0;

          assert (!lca->var_lca_list.first->same_lca_link.prev);
        }
      else
        {                       /* var == first == last */
          assert (var == lca->var_lca_list.last);

          lca->var_lca_list.last = lca->var_lca_list.first;

          assert (!lca->var_lca_list.first);
          assert (!lca->var_lca_list.last);
        }
    }

  assert (!var->same_lca_link.prev);
  assert (!var->same_lca_link.next);
}
#endif


/* 
- add variable 'var' to 'lca-child-list-occs' of all LCA-children
- TODO: adapt initial stack size? 
*/
void
add_variable_to_lca_child_list_occs_of_nodes (Nenofex * nenofex,
                                              Var * var,
                                              LCAObject * lca_object)
{
  Stack *var_pos_in_lca_child_list_occs = var->pos_in_lca_child_list_occs;
  assert (var_pos_in_lca_child_list_occs);
  reset_stack (var_pos_in_lca_child_list_occs);

  unsigned long int child_pos = 0;
  Node **ch, *child;
  for (ch = lca_object->children; (child = *ch); ch++, child_pos++)
    {
      Stack *child_lca_child_list_occs = child->lca_child_list_occs;
      Stack *child_pos_in_lca_children = child->pos_in_lca_children;

      if (!child_lca_child_list_occs)
        {                       /* TODO: adapt initial stack size? */
          assert (!child_pos_in_lca_children);
          child->lca_child_list_occs =
            child_lca_child_list_occs = create_stack (nenofex->mm, DEFAULT_STACK_SIZE);
          child->pos_in_lca_children =
            child_pos_in_lca_children = create_stack (nenofex->mm, DEFAULT_STACK_SIZE);
        }
      assert (child_pos_in_lca_children);

      push_stack (nenofex->mm, var_pos_in_lca_child_list_occs,
                  (void *) (unsigned long int)
                  count_stack (child_lca_child_list_occs));

      /* push 'var' on occ-stack, 'pos' of child in lca-children on pos-stack */
      assert (count_stack (child_lca_child_list_occs) ==
              count_stack (child_pos_in_lca_children));
      push_stack (nenofex->mm, child_lca_child_list_occs, var);
      push_stack (nenofex->mm, child_pos_in_lca_children, (void *) child_pos);

      assert (count_stack (child->lca_child_list_occs) ==
              count_stack (child->pos_in_lca_children));
    }                           /* end: for all LCA-children */

  assert (lca_object->num_children ==
          count_stack (var->pos_in_lca_child_list_occs));

#ifndef NDEBUG
#if ASSERT_ALL_LCA_OCC_POS_INTEGRITY
  assert_all_lca_occ_pos_integrity (nenofex);
#endif
#endif
}


/* 
- computes LCA over occs of a var and collects LCA's children containing these occs
- insert variable into LCA's variable list
*/
static void
find_variable_lca_and_children (Nenofex * nenofex, Var * var,
                                LCAObject * lca_object,
                                const int add_var_entry)
{
  assert (var);
  assert (variable_has_occs (var));

#ifndef NDEBUG
#if ASSERT_BEFORE_FIND_VAR_LCA_FULL_GRAPH_INTEGRITY
  assert_all_occ_lists_integrity (nenofex);
  assert_all_child_occ_lists_integrity (nenofex);
#endif
#endif

  assert (!lca_object->lca);
  assert (lca_object->num_children == 0);
  assert (lca_object->size_children != 0);
  assert (lca_object->top_p == lca_object->children);
  assert (!var->same_lca_link.prev);
  assert (!var->same_lca_link.next);

  Node *cur;

  for (cur = var->lits[0].occ_list.first; cur; cur = cur->occ_link.next)
    {                           /* neg. occ's */
      find_lca_and_children (nenofex, lca_object->lca, cur, lca_object);
    }

  for (cur = var->lits[1].occ_list.first; cur; cur = cur->occ_link.next)
    {                           /* pos. occ's */
      find_lca_and_children (nenofex, lca_object->lca, cur, lca_object);
    }

#ifndef NDEBUG
#if ASSERT_LCA_OBJECT_INTEGRITY
  assert_lca_object_integrity (nenofex, lca_object, var);
#endif
#endif

  unmark_lca_children (lca_object);

  add_variable_to_lca_list (nenofex, var);

  if (add_var_entry)
    add_variable_to_lca_child_list_occs_of_nodes (nenofex, var, lca_object);

#ifndef NDEBUG
#if ASSERT_ALL_LCA_CHILDREN_UNMARKED
  assert_all_lca_children_unmarked (lca_object);
#endif
#endif

#ifndef NDEBUG
#if ASSERT_AFTER_FIND_VAR_LCA_FULL_GRAPH_INTEGRITY
  assert_all_occ_lists_integrity (nenofex);
  assert_all_child_occ_lists_integrity (nenofex);
#endif
#endif
}


/* START: LCA-COMPUTATION OF NON-INNERMOST UNIVERSAL VARIABLES */

static void
mark_universal_lca_children (LCAObject * universal_lca_obj)
{
  Node **ch, *child;
  for (ch = universal_lca_obj->children; (child = *ch); ch++)
    {
      assert (!universal_lca_child_marked (child));
      mark_universal_lca_child (child);
    }
}


static void
unmark_universal_lca_children (LCAObject * universal_lca_obj)
{
  Node **ch, *child;
  for (ch = universal_lca_obj->children; (child = *ch); ch++)
    {
      assert (universal_lca_child_marked (child));
      unmark_universal_lca_child (child);
    }
}


static void
collect_depending_variable (Nenofex *nenofex, Stack * depending_existential_variables,
                            Var * var)
{
  if (!var->collected_as_depending)
    {
      var->collected_as_depending = 1;
      push_stack (nenofex->mm, depending_existential_variables, var);
    }
}


/*
- check lca-subformula of univ. var. and collect dep. vars. from innermost scope 
- VERY IMPORTANT that NO node is visited more than once during successive 
    calls of this function as typically happens during LCA-computation
*/
static void
collect_innermost_depending_existential_variables (Nenofex *nenofex, 
                                                   Var * universal_var,
                                                   Stack *
                                                   depending_existential_variables,
                                                   Stack *
                                                   dependency_marked_nodes)
{
  LCAObject *universal_lca_object = &universal_var->exp_costs.lca_object;
  /* NOTE: assertion will fail if units are not eliminated until saturation */
  assert (universal_lca_object->lca
          && !is_literal_node (universal_lca_object->lca));

  const unsigned int universal_nesting = universal_var->scope->nesting;
  Stack *stack = create_stack (nenofex->mm, DEFAULT_STACK_SIZE);

  Node **ch, *child;
  for (ch = universal_lca_object->children; (child = *ch); ch++)
    {
      if (!dependency_visit_marked (child))
        push_stack (nenofex->mm, stack, child);
    }

  Node *cur;
  while ((cur = pop_stack (stack)))
    {
      assert (!dependency_visit_marked (cur));

      if (is_literal_node (cur))
        {                       /* collect exist. variables if depending on cur. universal variable */
          Var *var = cur->lit->var;
          Scope *scope = var->scope;

          if (is_existential_scope (scope)
              && scope->nesting > universal_nesting)
            collect_depending_variable (nenofex, depending_existential_variables, var);
        }
      else                      /* op-node */
        {
          for (child = cur->child_list.last; child;
               child = child->level_link.prev)
            {
              if (!dependency_visit_marked (child))
                push_stack (nenofex->mm, stack, child);
            }
        }                       /* end: op-node */
    }                           /* end: while stack not empty */

  delete_stack (nenofex->mm, stack);

  if (dependency_marked_nodes)
    {                           /* mark current LCA and LCA-children as visited */
#if 0
      /* BUG FIX */
      Node *universal_lca = universal_lca_object->lca;
      if (!dependency_visit_marked (universal_lca))
        {
          mark_dependency_visit (universal_lca);
          push_stack (nenofex->mm, dependency_marked_nodes, universal_lca);
        }
#endif

      for (ch = universal_lca_object->children; (child = *ch); ch++)
        {
          if (!dependency_visit_marked (child))
            {
              mark_dependency_visit (child);
              push_stack (nenofex->mm, dependency_marked_nodes, child);
            }
        }                       /* end: for all LCA-children */
    }                           /* end: mark nodes as visited */
}


static void
unify_universal_lca_children (Nenofex *nenofex, LCAObject * universal_lca_object,
                              LCAObject * existential_lca_object)
{
  Node **ch, *child;
  for (ch = existential_lca_object->children; (child = *ch); ch++)
    {                           /* add children if not already contained */
      if (!universal_lca_child_marked (child))
        {
          mark_universal_lca_child (child);
          add_lca_child (nenofex, universal_lca_object, child);
        }
    }                           /* end: for */
}


/*
- computes LCA of a non-innermost univ. var. by merging two given LCAs
- by this way the LCA of such a universal variable is computed incrementally
- LCA of each depending existential variable is passed onto this function
- NOTE: EXACTLY the same algorithm as for maintaining current 'changed-subformula'
*/
static void
compute_universal_lca_by_unification (Nenofex * nenofex,
                                      Var * universal_var,
                                      LCAObject * universal_lca_object,
                                      LCAObject * existential_lca_object)
{
  assert (&universal_var->exp_costs.lca_object == universal_lca_object);

#if COMPUTE_LCA_PARENT_VISITS
  nenofex->stats.num_total_lca_algo_calls++;
#endif

  Node *universal_lca = universal_lca_object->lca;
  Node *existential_lca = existential_lca_object->lca;

  assert (universal_lca);
  assert (existential_lca);

  if (universal_lca == existential_lca)
    {
      unify_universal_lca_children (nenofex, universal_lca_object,
                                    existential_lca_object);
      return;
    }

  Node *high_node, *low_node, *high_node_prev, *low_node_prev;

  low_node_prev = 0;

  if (universal_lca->level >= existential_lca->level)
    {
      high_node = existential_lca;
      low_node = universal_lca;
    }
  else
    {
      high_node = universal_lca;
      low_node = existential_lca;
    }

  unsigned const int high_node_level = high_node->level;

  while (high_node_level < low_node->level)
    {                           /* check if high_node is reachable from low_node via parent-pointers */
#if COMPUTE_LCA_PARENT_VISITS
      nenofex->stats.num_total_lca_parent_visits++;
#endif
      low_node_prev = low_node;
      low_node = low_node->parent;
    }

  if (high_node == low_node)
    {                           /* check whether low_node is successor of an lca-child of 
                                   high_node or only of an "ordinary" child */

      if (high_node == universal_lca)
        {
          if (universal_lca_child_marked (low_node_prev))
            {                   /* nothing to be done: 'existential_lca' is contained in 'universal_lca' */
              ;
            }
          else
            {                   /* add child to universal_lca-children */
              mark_universal_lca_child (low_node_prev);
              add_lca_child (nenofex, universal_lca_object, low_node_prev);
            }
        }
      else                      /* high_node == existential_lca */
        {                       /* set 'universal_lca := existential_lca' */
          assert (high_node == existential_lca);

          /* must reset temporary univ. LCA-object and assign exist. LCA-object */
          unmark_universal_lca_children (universal_lca_object);
          unlink_variable_from_lca_list (universal_var);
          reset_lca_object (nenofex, universal_var, universal_lca_object, 0);

          Node **ch, *child;
          for (ch = existential_lca_object->children; (child = *ch); ch++)
            {
              assert (!universal_lca_child_marked (child));
              mark_universal_lca_child (child);
              add_lca_child (nenofex, universal_lca_object, child);
            }                   /* end: for */

          if (!universal_lca_child_marked (low_node_prev))
            {
              mark_universal_lca_child (low_node_prev);
              add_lca_child (nenofex, universal_lca_object, low_node_prev);
            }

          universal_lca_object->lca = existential_lca;
          add_variable_to_lca_list (nenofex, universal_var);

        }                       /* end: high_node == existential_lca */

    }
  else
    {                           /* need to find 'lca(universal_lca, existential_lca)' by 
                                   following parent-pointers in parallel */

      do
        {
#if COMPUTE_LCA_PARENT_VISITS
          nenofex->stats.num_total_lca_parent_visits += 2;
#endif
          low_node_prev = low_node;
          low_node = low_node->parent;

          high_node_prev = high_node;
          high_node = high_node->parent;

          assert (high_node);
          assert (low_node);
        }
      while (high_node != low_node);
      assert (high_node);

      unmark_universal_lca_children (universal_lca_object);
      unlink_variable_from_lca_list (universal_var);
      reset_lca_object (nenofex, universal_var, universal_lca_object, 0);

      universal_lca_object->lca = high_node;

      assert (!universal_lca_child_marked (low_node_prev));
      mark_universal_lca_child (low_node_prev);
      add_lca_child (nenofex, universal_lca_object, low_node_prev);

      assert (!universal_lca_child_marked (high_node_prev));
      mark_universal_lca_child (high_node_prev);
      add_lca_child (nenofex, universal_lca_object, high_node_prev);

      add_variable_to_lca_list (nenofex, universal_var);
    }                           /* end: compute 'lca(universal_lca, existential_lca)' */

  assert (!is_literal_node (universal_lca_object->lca));
}


#ifndef NDEBUG
static void
assert_no_var_collected_as_depending (Nenofex * nenofex)
{
  void **v_scope, **scope_end;
  scope_end = nenofex->scopes->top;
  for (v_scope = nenofex->scopes->elems; v_scope < scope_end; v_scope++)
    {
      Scope *scope = *v_scope;

      void **v_var, **var_end;
      var_end = scope->vars->top;
      for (v_var = scope->vars->elems; v_var < var_end; v_var++)
        {
          Var *var = *v_var;
          assert (!var->collected_as_depending);
        }                       /* end: for all vars */

    }                           /* end: for all scopes */
}
#endif /* end: ifndef NDEBUG */


#ifndef NDEBUG
static void
assert_universal_lca_computation_graph_and_vars (Nenofex * nenofex)
{
  Stack *stack = create_stack (nenofex->mm, DEFAULT_STACK_SIZE);
  push_stack (nenofex->mm, stack, nenofex->graph_root);

  Node *cur;
  while ((cur = pop_stack (stack)))
    {
      assert (!lca_child_marked (cur));
      assert (!universal_lca_child_marked (cur));
      assert (!dependency_visit_marked (cur));

      if (!is_literal_node (cur))
        {
          Node *child;
          for (child = cur->child_list.last; child;
               child = child->level_link.prev)
            push_stack (nenofex->mm, stack, child);
        }
    }                           /* end: while stack not empty */
  delete_stack (nenofex->mm, stack);

  assert_no_var_collected_as_depending (nenofex);
}
#endif /* end: ifndef NDEBUG */


static void
init_variable_scores (Nenofex * nenofex, Var * var,
                      const int update_key_priority_queue);


/* only a minor optimization */
#define OPTIMIZED_VAR_COLLECTION 1

/*
- for expansions of universal variables from non-innermost scope
*/
static void
find_non_innermost_universal_lca_and_children (Nenofex * nenofex,
                                               Var * universal_var)
{
#ifndef NDEBUG
#if ASSERT_UNIVERSAL_LCA_COMPUTATION_GRAPH_AND_VARS
  assert_universal_lca_computation_graph_and_vars (nenofex);
#endif
#endif
  assert (nenofex->next_scope && is_universal_scope (*nenofex->next_scope));
  assert (nenofex->cur_scope && is_existential_scope (*nenofex->cur_scope));
  assert (is_universal_scope (universal_var->scope) &&
          universal_var->scope->nesting < (*nenofex->cur_scope)->nesting);

  LCAObject *universal_lca_object = &universal_var->exp_costs.lca_object;
  Stack *depending_existential_variables = create_stack (nenofex->mm, DEFAULT_STACK_SIZE);
  Stack *processed_existential_variables = create_stack (nenofex->mm, DEFAULT_STACK_SIZE);
  Stack *dependency_marked_nodes = create_stack (nenofex->mm, DEFAULT_STACK_SIZE);

  /* first compute lca of univ. var. in standard way, 
     but do NOT add var. to lca-children yet */
  find_variable_lca_and_children (nenofex, universal_var,
                                  universal_lca_object, 0);
  mark_universal_lca_children (universal_lca_object);
  collect_innermost_depending_existential_variables (nenofex, universal_var,
                                                     depending_existential_variables,
                                                     dependency_marked_nodes);

  Var *depending_var;

#if OPTIMIZED_VAR_COLLECTION
  while (count_stack (depending_existential_variables))
    {
#endif

      while ((depending_var = pop_stack (depending_existential_variables)))
        {
          /* need to store processed vars for unmarking AFTERWARDS */
          push_stack (nenofex->mm, processed_existential_variables, depending_var);

          assert (is_existential_scope (depending_var->scope));
          assert (depending_var->scope->nesting >
                  universal_var->scope->nesting);

          LCAObject *existential_lca_object =
            &depending_var->exp_costs.lca_object;

          if (!existential_lca_object->lca)
            {                   /* compute LCA of depending var from scratch */
              find_variable_lca_and_children (nenofex, depending_var,
                                              existential_lca_object, 1);
            }
          else if (lca_update_marked (depending_var))
            {                   /* reset + compute lca of depending var. */
              unlink_variable_from_lca_list (depending_var);
              reset_lca_object (nenofex, depending_var,
                                existential_lca_object, 1);
              find_variable_lca_and_children (nenofex, depending_var,
                                              existential_lca_object, 1);
              lca_update_unmark (depending_var);
            }

          /* next, unify both LCAs to get extended universal LCA */
          compute_universal_lca_by_unification (nenofex, universal_var,
                                                universal_lca_object,
                                                existential_lca_object);

#if OPTIMIZED_VAR_COLLECTION
        }                       /* end: inner while: lca-computation  */
#endif

      /* now, 'universal_lca_object' holds current univ. LCA; 
         next, once again collect depending variables */
      collect_innermost_depending_existential_variables (nenofex, universal_var,
                                                         depending_existential_variables,
                                                         dependency_marked_nodes);
    }                           /* end: outer while: while not all depending variables processed */

  /* univ. LCA has been computed; next, unmark lca-children 
     and add variable entries */
  unmark_universal_lca_children (universal_lca_object);
  add_variable_to_lca_child_list_occs_of_nodes (nenofex, universal_var,
                                                universal_lca_object);

  /* unmark collected depending variables */
  while ((depending_var = pop_stack (processed_existential_variables)))
    {
      assert (depending_var->collected_as_depending);
      depending_var->collected_as_depending = 0;
    }

  Node *node;
  while ((node = pop_stack (dependency_marked_nodes)))
    {
      assert (dependency_visit_marked (node));
      unmark_dependency_visit (node);
    }

  delete_stack (nenofex->mm, depending_existential_variables);
  delete_stack (nenofex->mm, processed_existential_variables);
  delete_stack (nenofex->mm, dependency_marked_nodes);

#ifndef NDEBUG
#if ASSERT_UNIVERSAL_LCA_COMPUTATION_GRAPH_AND_VARS
  assert_universal_lca_computation_graph_and_vars (nenofex);
#endif
#endif
}

/* END: LCA-COMPUTATION OF NON-INNERMOST UNIVERSAL VARIABLES */


#ifndef NDEBUG
/* 
- for assertion checking only
*/
static unsigned int
count_children (Nenofex * nenofex, Node * node)
{
  assert (node);

  unsigned int result = 0;

  if (is_literal_node (node))   /* literal might be marked so loop would be entered */
    return result;

  Node *child;
  for (child = node->child_list.first; child; child = child->level_link.next)
    result++;

  return result;
}
#endif /* end ifndef NDEBUG */


/*
- when copying literal nodes (universal expansion): must check whether var. 
    has been copied or not (i.e. depends on expanded univ. var.)
*/
static Node *
copy_node (Nenofex * nenofex, Node * node)
{
  Node *copy = 0;

  switch (node->type)
    {
    case NODE_TYPE_LITERAL:
      {
        assert (node->id == node->lit->negated ?
                -node->lit->var->id : node->lit->var->id);
        Var *var = node->lit->var;

        copy = lit_node (nenofex, node->id, var->copied ? var->copied : var);
        copy->size_subformula = node->size_subformula;
        /* level, parent and occ_links will be set when adding to an op-node */
        break;
      }
    case NODE_TYPE_AND:
      {
        copy = and_node (nenofex);
        copy->level = node->level;
        copy->id = node->id;
        copy->size_subformula = node->size_subformula;
        nenofex->next_free_node_id--;
        break;
      }
    case NODE_TYPE_OR:
      {
        copy = or_node (nenofex);
        copy->level = node->level;
        copy->id = node->id;
        copy->size_subformula = node->size_subformula;
        nenofex->next_free_node_id--;
        break;
      }
    default:
      assert (0);
    }                           /* end: switch */

  return copy;
}


#ifndef NDEBUG
/*
- for assertion checking only
*/
void
assert_copy_equals (Nenofex * nenofex, Node * original, Node * copy)
{
  Stack *stack1 = create_stack (nenofex->mm, 16);
  Stack *stack2 = create_stack (nenofex->mm, 16);
  push_stack (nenofex->mm, stack1, (void *) original);
  push_stack (nenofex->mm, stack2, (void *) copy);

  Node *cur1, *cur2;
  while ((cur1 = pop_stack (stack1)))
    {
      cur2 = pop_stack (stack2);
      assert (cur2);
      assert (cur1->type == cur2->type);
      assert (cur1->level == cur2->level);
      assert (cur1->num_children == cur2->num_children);
      assert (cur1->size_subformula == cur2->size_subformula);

      if (is_literal_node (cur1))
        {
          assert (cur1->id == cur2->id);
        }
      else
        {
          assert (cur1->id == cur2->id);
          Node *child;
          unsigned int cnt1, cnt2;
          cnt1 = cnt2 = 0;
          for (child = cur1->child_list.last; child;
               child = child->level_link.prev)
            {
              push_stack (nenofex->mm, stack1, (void *) child);
              cnt1++;
            }
          for (child = cur2->child_list.last; child;
               child = child->level_link.prev)
            {
              push_stack (nenofex->mm, stack2, (void *) child);
              cnt2++;
            }
          assert (cnt1 == cnt2);
        }
    }                           /* end: while */

  assert (!count_stack (stack1));
  assert (!count_stack (stack2));
  delete_stack (nenofex->mm, stack1);
  delete_stack (nenofex->mm, stack2);
}
#endif


static void
add_node_to_child_list_before (Nenofex * nenofex, Node * child,
                               Node * new_child);


static void
add_lit_node_to_occurrence_list (Nenofex * nenofex, Node * new_occ);


/* 
- called in order to copy a formula (subgraph)
- simple copying, no marking as in 'copy_formula_mark_propagation' 
*/
static Node *
copy_formula (Nenofex * nenofex, Node * root)
{
  Stack *node_stack = create_stack (nenofex->mm, DEFAULT_STACK_SIZE);        /* nodes to be visited */
  Stack *copy_stack = create_stack (nenofex->mm, DEFAULT_STACK_SIZE);        /* copied nodes */
  Node *result;

  push_stack (nenofex->mm, node_stack, root);

  Node *cur;
  while ((cur = pop_stack (node_stack)))
    {
      if (is_literal_node (cur))
        {
          assert (!cur->lit->var->copied);
          result = copy_node (nenofex, cur);
          push_stack (nenofex->mm, copy_stack, result);
        }
      else
        {                       /* op-node -> copy children first */
          if (!copy_formula_marked (cur))
            {
              copy_formula_mark (cur);
              push_stack (nenofex->mm, node_stack, cur);

              Node *child;
              for (child = cur->child_list.last; child;
                   child = child->level_link.prev)
                {
                  push_stack (nenofex->mm, node_stack, child);
                }
            }
          else                  /* all children have been copied -> create OP-node */
            {
              copy_formula_unmark (cur);
              result = copy_node (nenofex, cur);

              assert (!result->child_list.first);
              assert (result->child_list.first == result->child_list.last);

              Node *child = pop_stack (copy_stack);
              add_node_to_child_list (nenofex, result, child);

              if (is_literal_node (child))
                add_lit_node_to_occurrence_list (nenofex, child);

              unsigned int cnt = cur->num_children - 1;
              unsigned int i;

              for (i = 0; i < cnt; i++)
                {
                  child = pop_stack (copy_stack);
                  add_node_to_child_list_before (nenofex,
                                                 result->child_list.first,
                                                 child);

                  if (is_literal_node (child))
                    add_lit_node_to_occurrence_list (nenofex, child);
                }

              push_stack (nenofex->mm, copy_stack, result);
            }
        }                       /* end: is op-node */
    }                           /* end: while */

  result = pop_stack (copy_stack);
  assert (result);

  if (is_literal_node (result))
    {                           /* special case: root is a literal */
      assert (is_literal_node (root));

      result->level = root->level;
      add_lit_node_to_occurrence_list (nenofex, result);
    }

  assert (!count_stack (copy_stack));
  assert (!count_stack (node_stack));

  delete_stack (nenofex->mm, node_stack);
  delete_stack (nenofex->mm, copy_stack);

#ifndef NDEBUG
#if ASSERT_COPY_EQUALS
  assert_copy_equals (nenofex, root, result);
#endif
#endif

  return result;
}


/* 
- called in order to copy a formula (subgraph) during expansion
- copy subformula and mark literals for forthcoming propagation
- copying and marking has been merged in this function 
*/
static Node *
copy_formula_mark_propagation (Nenofex * nenofex, Node * root,
                               Var * expanded_var)
{
  Stack *node_stack = create_stack (nenofex->mm, DEFAULT_STACK_SIZE);        /* nodes to be visited */
  Stack *copy_stack = create_stack (nenofex->mm, DEFAULT_STACK_SIZE);        /* copied nodes */
  Node *result;

  push_stack (nenofex->mm, node_stack, root);

  Node *cur;
  while ((cur = pop_stack (node_stack)))
    {
      if (is_literal_node (cur))
        {
          result = copy_node (nenofex, cur);
          Var *var = result->lit->var;

          assert (!cur->lit->var->copied || cur->lit->var->copied == var);

          /* copied literals will be assigned 'true' in forthcoming propagation */
          if (var == expanded_var)
            truth_propagation_mark (result);
          else
            {
              lca_update_mark (var);
              inc_score_update_mark (var);
              dec_score_update_mark (var);
              collect_variable_for_update (nenofex, var);
            }

          push_stack (nenofex->mm, copy_stack, result);
        }
      else
        {                       /* op-node -> copy children first */
          if (!copy_formula_marked (cur))
            {
              copy_formula_mark (cur);
              push_stack (nenofex->mm, node_stack, cur);

              Node *child;
              for (child = cur->child_list.last; child;
                   child = child->level_link.prev)
                {
                  push_stack (nenofex->mm, node_stack, child);
                }
            }
          else                  /* all children have been copied -> create OP-node */
            {
              copy_formula_unmark (cur);
              result = copy_node (nenofex, cur);

              assert (!result->child_list.first);
              assert (result->child_list.first == result->child_list.last);

              Node *child = pop_stack (copy_stack);
              add_node_to_child_list (nenofex, result, child);

              if (is_literal_node (child))
                add_lit_node_to_occurrence_list (nenofex, child);

              unsigned int cnt = cur->num_children - 1;
              unsigned int i;

              for (i = 0; i < cnt; i++)
                {
                  child = pop_stack (copy_stack);
                  add_node_to_child_list_before (nenofex,
                                                 result->child_list.first,
                                                 child);

                  if (is_literal_node (child))
                    add_lit_node_to_occurrence_list (nenofex, child);
                }

              push_stack (nenofex->mm, copy_stack, result);
            }
        }                       /* end: is op-node */
    }                           /* end: while */

  result = pop_stack (copy_stack);
  assert (result);

  if (is_literal_node (result))
    {                           /* special case: root is a literal */
      assert (is_literal_node (root));

      result->level = root->level;
      add_lit_node_to_occurrence_list (nenofex, result);
    }

  assert (!count_stack (copy_stack));
  assert (!count_stack (node_stack));

  delete_stack (nenofex->mm, node_stack);
  delete_stack (nenofex->mm, copy_stack);

#ifndef NDEBUG
#if ASSERT_COPY_EQUALS
  assert_copy_equals (nenofex, root, result);
#endif
#endif

  return result;
}


/*
- traverse subformula rooted at 'root' and set levels
*/
void
update_level (Nenofex * nenofex, Node * root)
{
  assert (root);
  assert (root->parent);

  Stack *stack = create_stack (nenofex->mm, DEFAULT_STACK_SIZE);
  push_stack (nenofex->mm, stack, root);

  Node *cur;
  while ((cur = pop_stack (stack)))
    {
      cur->level = cur->parent->level + 1;
      if (!is_literal_node (cur))
        {
          Node *child;
          for (child = cur->child_list.last; child;
               child = child->level_link.prev)
            push_stack (nenofex->mm, stack, child);
        }
    }                           /* end: while */

  delete_stack (nenofex->mm, stack);
}


#ifndef NDEBUG

/*
- for assertion checking only
*/
static void
assert_expand_node_integrity (Nenofex * nenofex, Node * parent)
{
  assert (parent->num_children == count_children (nenofex, parent));

  if (is_literal_node (parent))
    {
      assert (!parent->child_list.last);
      assert (parent->lit);
      assert (parent->id);
      assert (parent->lit->negated || parent->id > 0);
      assert (!parent->lit->negated || parent->id < 0);
      assert (parent->id == (parent->lit->negated ?
                             -parent->lit->var->id : parent->lit->var->id));
      assert (parent->lit->occ_list.first);
      assert (parent->lit->occ_list.last);
      assert (parent->occ_link.next || parent->lit->occ_list.last == parent);
      assert (parent->occ_link.prev || parent->lit->occ_list.first == parent);
    }
  else
    {
      assert (parent->id > 0);
      assert (!parent->lit);
      assert ((unsigned int) parent->id > nenofex->num_orig_vars);
      assert (is_or_node (parent) || is_and_node (parent));
      if (!parent->child_list.first)
        {
          assert (!parent->child_list.last);
          assert (0);
        }
      else
        {
          assert (parent->child_list.last);
          Node *ch, *prev;
          prev = 0;
          for (ch = parent->child_list.first; ch; ch = ch->level_link.next)
            {
              assert (!prev || ch->level_link.prev == prev);
              assert (!prev || prev->level_link.next == ch);
              assert (ch->parent->type != ch->type);
              assert (ch->parent == parent);
              assert (ch->level == parent->level + 1);
              assert (ch != parent->child_list.first || !ch->level_link.prev);
              assert (ch != parent->child_list.last || !ch->level_link.next);
              prev = ch;
            }
        }
    }                           /* end: has children */
}


/*
- for assertion checking only
*/
static void
assert_expand_graph_integrity (Nenofex * nenofex)
{
  Stack *stack = create_stack (nenofex->mm, DEFAULT_STACK_SIZE);
  push_stack (nenofex->mm, stack, nenofex->graph_root);

  Node *cur;
  while ((cur = pop_stack (stack)))
    {
      assert_expand_node_integrity (nenofex, cur);

      if (!is_literal_node (cur))
        {
          Node *child;
          for (child = cur->child_list.last; child;
               child = child->level_link.prev)
            {
              push_stack (nenofex->mm, stack, child);
            }
        }
    }                           /* end: while stack not empty */

  delete_stack (nenofex->mm, stack);
}
#endif /* end ifndef NDEBUG */


static void
propagate_truth (Nenofex * nenofex, Node * occ)
{
  assert (occ);
  assert (is_literal_node (occ));

  Node *nenofex_graph_root = nenofex->graph_root;

  if (occ == nenofex_graph_root)
    {
      nenofex->result = NENOFEX_RESULT_SAT;
      remove_and_free_subformula (nenofex, occ);
      return;
    }

  Node *occ_parent = occ->parent;

  if (is_or_node (occ_parent))
    {
      /* BUG-FIX */
      if (occ_parent == nenofex_graph_root)
        nenofex->result = NENOFEX_RESULT_SAT;

      remove_and_free_subformula (nenofex, occ_parent);

      if (!nenofex->graph_root)
        {                       /* graph-root might have been deleted during merging / 1-l-simp */
          /* BUG FIX  --nenofex->result = NENOFEX_RESULT_SAT; */
          assert (nenofex->result != NENOFEX_RESULT_UNKNOWN);
        }
    }
  else                          /* parent is AND */
    {
      remove_and_free_subformula (nenofex, occ);
    }
}


static void
propagate_falsity (Nenofex * nenofex, Node * occ)
{
  assert (occ);
  assert (is_literal_node (occ));

  Node *nenofex_graph_root = nenofex->graph_root;

  if (occ == nenofex_graph_root)
    {
      nenofex->result = NENOFEX_RESULT_UNSAT;
      remove_and_free_subformula (nenofex, occ);
      return;
    }

  Node *occ_parent = occ->parent;

  if (is_and_node (occ_parent))
    {
      /* BUG-FIX */
      if (occ_parent == nenofex_graph_root)
        nenofex->result = NENOFEX_RESULT_UNSAT;

      remove_and_free_subformula (nenofex, occ_parent);

      if (!nenofex->graph_root)
        {                       /* graph-root might have been deleted during merging / 1-l-simp */
          /* BUG FIX  --nenofex->result = NENOFEX_RESULT_UNSAT; */
          assert (nenofex->result != NENOFEX_RESULT_UNKNOWN);
        }
    }
  else                          /* parent is OR */
    {
      remove_and_free_subformula (nenofex, occ);
    }
}


/*
- propagate variable assignment
- NOTE: could eliminate check for truth mark since all new 
    occurrences are appended to occ-list during expansion 
*/
static void
propagate_literals (Nenofex * nenofex, Var * var)
{
  Node *occ;
  Lit *lit;

  lit = var->lits;
  assert (lit->negated);
  while ((occ = lit->occ_list.first))
    {                           /* negative occurrences */
      assert (is_literal_node (occ));

      if (truth_propagation_marked (occ))
        propagate_falsity (nenofex, occ);
      else
        propagate_truth (nenofex, occ);
    }

  lit = var->lits + 1;
  assert (!lit->negated);
  while ((occ = lit->occ_list.first))
    {                           /* positive occurrences */
      assert (is_literal_node (occ));

      if (truth_propagation_marked (occ))
        propagate_truth (nenofex, occ);
      else
        propagate_falsity (nenofex, occ);
    }
}


#ifndef NDEBUG
/*
- for assertion checking only
- returns number of nodes in subformula rooted at 'root'
*/
unsigned int
subformula_size (Nenofex * nenofex, Node * root)
{
  Stack *stack = create_stack (nenofex->mm, DEFAULT_STACK_SIZE);
  unsigned int result = 0;

  push_stack (nenofex->mm, stack, root);

  Node *cur;
  while ((cur = pop_stack (stack)))
    {
      result++;
      if (!is_literal_node (cur))
        {
          Node *ch;
          for (ch = cur->child_list.last; ch; ch = ch->level_link.prev)
            {
              push_stack (nenofex->mm, stack, ch);
            }
        }
    }                           /* end: while */
  delete_stack (nenofex->mm, stack);
  return result;
}
#endif /* end ifndef NDEBUG */


static Scope *
find_innermost_non_empty_scope (Nenofex * nenofex)
{
  Scope **scope;
  for (scope = (Scope **) nenofex->scopes->top - 1;
       scope >= (Scope **) nenofex->scopes->elems && (*scope)->is_empty;
       scope--)
    ;

  assert (scope >= (Scope **) nenofex->scopes->elems);

  return *scope;
}


/*
- TODO: incremental version
*/
static int
is_empty_scope (Nenofex * nenofex, Scope * scope)
{
  Var **var, **start;
  start = (Var **) scope->vars->elems;

  for (var = (Var **) scope->vars->top - 1;
       var >= start && ((!variable_has_occs (*var)) || (*var)->eliminated);
       var--)
    ;

#if 1
  assert (nenofex->result != NENOFEX_RESULT_UNKNOWN ||
          !scope->is_empty || var == (Var **) scope->vars->elems - 1);
  assert (nenofex->result != NENOFEX_RESULT_UNKNOWN ||
          var != (Var **) scope->vars->elems - 1 || scope->is_empty);
#endif

  assert (nenofex->result != NENOFEX_RESULT_UNKNOWN ||
          var != (Var **) scope->vars->elems - 1
          || scope->remaining_var_cnt == 0);
  assert (nenofex->result != NENOFEX_RESULT_UNKNOWN
          || scope->remaining_var_cnt != 0
          || var == (Var **) scope->vars->elems - 1);

  return (var == (Var **) scope->vars->elems - 1);
}


/*
- mark variables for cost update
- from root of subformula where graph was modified, up to graph root
- check if encountered nodes are LCA of a variable
- TODO: clarify failed assertions
*/
void
mark_affected_scope_variables_for_cost_update (Nenofex * nenofex,
                                               Node * exp_root)
{
  assert (exp_root);

  Node *prev = exp_root;
  Node *cur = exp_root->parent;

  /* if cur has no parent at beginning (i.e. is at root), 
     then if there is a var that has lca == cur, 
     it is already marked if it has occs in the current subformula
   */

  while (cur)
    {
      Stack *lca_child_list_occs = prev->lca_child_list_occs;

      /* FAILED: possibly same reason as in ATPG    
         --assert(!lca_child_list_occs || !count_stack(lca_child_list_occs) || 
         cur->var_lca_list.first); */

      if (lca_child_list_occs)
        {
          /* NOT SURE */
          /*
             assert(!count_stack(lca_child_list_occs) || cur->var_lca_list.first);
             assert(!count_stack(lca_child_list_occs) || cur->var_lca_list.last);
           */

          void **v_var, **end;
          end = lca_child_list_occs->top;

          for (v_var = lca_child_list_occs->elems; v_var < end; v_var++)
            {
              Var *var = *v_var;
              inc_score_update_mark (var);
              collect_variable_for_update (nenofex, var);
            }                   /* end: for all variables where parent is lca */

        }                       /* end: cur is lca of at least one variable */

      assert (!is_literal_node (prev) || !prev->child_list.first);

      /* search for lits at path node -> vars have to be marked for dec-score update */
      Node *ch;
      for (ch = prev->child_list.first;
           ch && is_literal_node (ch); ch = ch->level_link.next)
        {
          Var *var = ch->lit->var;
          if (var->exp_costs.lca_object.lca)    /* BUG FIX */
            {
              dec_score_update_mark (var);
              collect_variable_for_update (nenofex, var);
            }
        }                       /* end: for all literals */

      prev = cur;
      cur = cur->parent;
    }                           /* end: while root of graph not checked */

  /* search for lits at path node -> vars have to be marked for dec-score update */
  Node *ch;
  for (ch = prev->child_list.first; ch && is_literal_node (ch);
       ch = ch->level_link.next)
    {
      Var *var = ch->lit->var;
      if (var->exp_costs.lca_object.lca)        /* BUG FIX */
        {
          dec_score_update_mark (var);
          collect_variable_for_update (nenofex, var);
        }
    }                           /* end: for all literals */
}


/*
- could be done incrementally
- checks whether lca(var) has occurrence of 'var' as child
- NOTE: must handle situation for non-innermost universal vars
*/
static Node *
lca_children_contain_lit (Var * var, LCAObject * lca_object)
{
  assert (lca_object->children);
  assert (lca_object->lca);

  Node **ch, *child;
  for (ch = lca_object->children; (child = *ch); ch++)
    {
      if (is_literal_node (child) && child->lit->var == var)
        break;
    }

  return child;
}


/*
- traverse subformula and mark encountered variables
- needed during a special case of variable-expansion
*/
static void
mark_occs_propagation_var_cost_update (Nenofex * nenofex, Var * var,
                                       const int mark_var_truth)
{
  assert (mark_var_truth == 0 || mark_var_truth == 1);
  assert (var->exp_costs.lca_object.lca);

  Stack *stack = create_stack (nenofex->mm, DEFAULT_STACK_SIZE);
  push_stack (nenofex->mm, stack, var->exp_costs.lca_object.lca);

  Node *cur;
  while ((cur = pop_stack (stack)))
    {
      if (is_literal_node (cur))
        {
          Var *cur_var = cur->lit->var;

          if (cur_var == var && mark_var_truth)
            truth_propagation_mark (cur);
          else if (cur_var != var)
            {
              lca_update_mark (cur_var);
              inc_score_update_mark (cur_var);
              dec_score_update_mark (cur_var);
              collect_variable_for_update (nenofex, cur_var);
            }
        }
      else
        {
          Node *ch;
          for (ch = cur->child_list.last; ch; ch = ch->level_link.prev)
            push_stack (nenofex->mm, stack, ch);
        }
    }                           /* end: while stack not empty */

  delete_stack (nenofex->mm, stack);
}


/* FUNCTIONS FOR MAINTAINING 'CHANGED-SUBFORMULA'
- changed-subformula: the region of the graph where changes occurred 
- represented by an LCAObject (like LCA of variable)
*/

/*
- nodes which are children of LCA of 'changed-subformula' 
    have pointer to position in child-list
- assign position for all node
*/
static void
set_pos_in_changed_child_list (Nenofex * nenofex)
{
  Node **ch, *child;
  for (ch = nenofex->changed_subformula.children; (child = *ch); ch++)
    {
      child->changed_ch_list_pos = ch;
    }
}


#ifndef NDEBUG
/*
- for assertion checking only
*/
static void
assert_pos_in_changed_ch_list (Nenofex * nenofex)
{
  Node **ch, *child;
  for (ch = nenofex->changed_subformula.children; (child = *ch); ch++)
    {
      assert (child->changed_ch_list_pos == ch);
    }
}
#endif /* end ifndef NDEBUG */


/*
- given LCAObject represents 'changed-subformula'
*/
static void
assign_changed_subformula (Nenofex * nenofex, LCAObject * lca_object)
{
  LCAObject *changed_subformula = &nenofex->changed_subformula;

  assert (!changed_subformula->lca);
  assert (changed_subformula->children);
  assert (!is_literal_node (lca_object->lca));
  assert (lca_object->num_children >= 2);

  reset_changed_lca_object (nenofex);

  assert (changed_subformula->top_p == changed_subformula->children);
  assert (changed_subformula->num_children == 0);
  assert (*(changed_subformula->children) == 0);

  int realloc_called =
    (changed_subformula->size_children <= lca_object->num_children) ? 1 : 0;

#ifndef NDEBUG
  unsigned int old_size = changed_subformula->size_children;
#endif

  Node **ch, *child;

  if (realloc_called)
    {
      for (ch = lca_object->children; (child = *ch); ch++)
        {                       /* add nodes */
          add_lca_child (nenofex, changed_subformula, child);
        }                       /* end: for */

      set_pos_in_changed_child_list (nenofex);
    }
  else                          /* no realloc of memory will occur -> may set pointer to pos during copying */
    {
      Node **pos = changed_subformula->top_p;

      for (ch = lca_object->children; (child = *ch); ch++)
        {                       /* add nodes and set position */
          child->changed_ch_list_pos = pos++;
          add_lca_child (nenofex, changed_subformula, child);
        }                       /* end: for */

      assert (pos ==
              changed_subformula->children +
              changed_subformula->num_children);
    }

#ifndef NDEBUG
  assert (!realloc_called || old_size != changed_subformula->size_children);
  assert (realloc_called || old_size == changed_subformula->size_children);
#endif

#ifndef NDEBUG
#if ASSERT_POS_IN_CHANGED_CH_LIST
  assert_pos_in_changed_ch_list (nenofex);
#endif
#endif

  assert (changed_subformula->num_children >= 2);
  assert (changed_subformula->top_p ==
          changed_subformula->children + changed_subformula->num_children);

  changed_subformula->lca = lca_object->lca;

  assert (!is_literal_node (nenofex->changed_subformula.lca));
}


static void
unify_changed_lca_children (Nenofex * nenofex, LCAObject * lca_object)
{
  LCAObject *changed_subformula = &(nenofex->changed_subformula);

  int realloc_possible =
    ((changed_subformula->size_children - changed_subformula->num_children) <=
     lca_object->num_children) ? 1 : 0;

  Node **ch, *child;
  if (realloc_possible)
    {
      for (ch = lca_object->children; (child = *ch); ch++)
        {                       /* add children if not already contained */
          if (!child->changed_ch_list_pos)
            add_lca_child (nenofex, changed_subformula, child);
        }                       /* end: for */

      set_pos_in_changed_child_list (nenofex);
    }
  else
    {
      Node **pos = changed_subformula->top_p;

      for (ch = lca_object->children; (child = *ch); ch++)
        {                       /* add children if not already contained */
          if (!child->changed_ch_list_pos)
            {
              child->changed_ch_list_pos = pos++;
              add_lca_child (nenofex, changed_subformula, child);
            }
        }                       /* end: for */
    }

#ifndef NDEBUG
#if ASSERT_POS_IN_CHANGED_CH_LIST
  assert_pos_in_changed_ch_list (nenofex);
#endif
#endif
}


static void
remove_changed_lca_child (Nenofex * nenofex, Node * node)
{
  Node **pos = node->changed_ch_list_pos;
  LCAObject *changed_subformula = &(nenofex->changed_subformula);

  assert (pos);

  assert (changed_subformula->num_children <
          changed_subformula->size_children);
  assert (changed_subformula->top_p > changed_subformula->children);

#ifndef NDEBUG
  if (nenofex->cur_expanded_var)
    {
      /* need a kind of workaround in following assertions; during expansion we 
         might have to remove nodes from changed-child-list */
      assert (changed_subformula->lca ==
              nenofex->cur_expanded_var->exp_costs.lca_object.lca
              || changed_subformula->num_children >= 2);
      assert (changed_subformula->lca ==
              nenofex->cur_expanded_var->exp_costs.lca_object.lca
              || changed_subformula->top_p >=
              changed_subformula->children + 2);
    }
  else
    {
      assert (changed_subformula->num_children >= 2);
      assert (changed_subformula->top_p >= changed_subformula->children + 2);
    }
#endif

  assert (*changed_subformula->top_p == 0);
  assert (changed_subformula->num_children ==
          (unsigned int) (changed_subformula->top_p -
                          changed_subformula->children));

  changed_subformula->num_children--;
  changed_subformula->top_p--;  /* last element overwrites the one to be deleted */

  (*pos)->changed_ch_list_pos = 0;      /* reset pointer of node to be removed */

  if (pos != changed_subformula->top_p)
    {                           /* average case; else, simply cut off last element */
      *pos = *changed_subformula->top_p;
      (*pos)->changed_ch_list_pos = pos;
    }

  *changed_subformula->top_p = 0;

  assert (changed_subformula->top_p >= changed_subformula->children);

#ifndef NDEBUG
#if ASSERT_POS_IN_CHANGED_CH_LIST
  assert_pos_in_changed_ch_list (nenofex);
#endif
#endif
}


static void
replace_changed_lca_child (Nenofex * nenofex, Node * old_node,
                           Node * new_node)
{
  Node **old_pos = old_node->changed_ch_list_pos;
  LCAObject *changed_subformula = &(nenofex->changed_subformula);

  assert (!new_node->changed_ch_list_pos);
  assert (old_pos);

  assert (changed_subformula->num_children <
          changed_subformula->size_children);
  assert (changed_subformula->num_children >= 2);
  assert (changed_subformula->top_p >= changed_subformula->children + 2);
  assert (*changed_subformula->top_p == 0);
  assert (changed_subformula->num_children ==
          (unsigned int) (changed_subformula->top_p -
                          changed_subformula->children));

  old_node->changed_ch_list_pos = 0;    /* reset pointer of old node */

  *old_pos = new_node;
  new_node->changed_ch_list_pos = old_pos;

#ifndef NDEBUG
#if ASSERT_POS_IN_CHANGED_CH_LIST
  assert_pos_in_changed_ch_list (nenofex);
#endif
#endif

  assert (changed_subformula->num_children >= 2);
  assert (changed_subformula->top_p ==
          changed_subformula->children + changed_subformula->num_children);
}


void
add_changed_lca_child (Nenofex * nenofex, Node * node)
{
  LCAObject *changed_subformula = &(nenofex->changed_subformula);
  int realloc_called =
    changed_subformula->num_children ==
    changed_subformula->size_children - 1 ? 1 : 0;

  assert (!node->changed_ch_list_pos);

#ifndef NDEBUG
  unsigned int old_size = changed_subformula->size_children;
#endif

  add_lca_child (nenofex, changed_subformula, node);

  if (realloc_called)
    set_pos_in_changed_child_list (nenofex);
  else
    node->changed_ch_list_pos = changed_subformula->top_p - 1;

  assert (node->changed_ch_list_pos == changed_subformula->top_p - 1);

#ifndef NDEBUG
  assert (!realloc_called || old_size != changed_subformula->size_children);
#endif

#ifndef NDEBUG
#if ASSERT_POS_IN_CHANGED_CH_LIST
  assert_pos_in_changed_ch_list (nenofex);
#endif
#endif
}


void
reset_changed_lca_object (Nenofex * nenofex)
{
  LCAObject *lca_object = &(nenofex->changed_subformula);

  Node **ch, *child;
  for (ch = lca_object->children; (child = *ch); ch++)
    {
      assert (child->changed_ch_list_pos == ch);

      child->changed_ch_list_pos = 0;
      *ch = 0;
    }

  lca_object->num_children = 0;
  lca_object->top_p = lca_object->children;
  lca_object->lca = 0;
}


static void
update_changed_subformula (Nenofex * nenofex, LCAObject * lca_object)
{
  LCAObject *changed_subformula = &(nenofex->changed_subformula);

  Node *changed_lca_cur = changed_subformula->lca;
  Node *changed_lca_new = lca_object->lca;

  assert (changed_lca_cur);
  assert (changed_lca_new);

  if (changed_lca_cur == changed_lca_new)
    {
      unify_changed_lca_children (nenofex, lca_object);
      return;
    }

  Node *high_node, *low_node, *high_node_prev, *low_node_prev;

  low_node_prev = 0;

  if (changed_lca_cur->level >= changed_lca_new->level)
    {
      high_node = changed_lca_new;
      low_node = changed_lca_cur;
    }
  else
    {
      high_node = changed_lca_cur;
      low_node = changed_lca_new;
    }

  unsigned const int high_node_level = high_node->level;

  while (high_node_level < low_node->level)
    {                           /* level-balancing -> check if high_node is reachable 
                                   from low_nide via parent-pointers */
      low_node_prev = low_node;
      low_node = low_node->parent;
    }

  if (high_node == low_node)
    {                           /* check whether low_node is successor of an lca-child of 
                                   high node or only of an "ordinary" child */

      if (high_node == changed_lca_cur)
        {
          if (low_node_prev->changed_ch_list_pos)
            {                   /* nothing to be done: 'changed_lca_new' contained in 'changed_lca_cur' */
              ;
            }
          else
            {                   /* add child to changed_lca-children */
              add_changed_lca_child (nenofex, low_node_prev);
            }
        }
      else                      /* high_node == changed_lca_new */
        {                       /* set 'changed_lca := changed_lca_new' */
          assert (high_node == changed_lca_new);

          changed_subformula->lca = 0;
          assign_changed_subformula (nenofex, lca_object);

          if (!low_node_prev->changed_ch_list_pos)
            add_changed_lca_child (nenofex, low_node_prev);

        }                       /* end: high_node == changed_lca_new */

    }
  else
    {                           /* need to find 'lca(changed_cur, changed_new)' by 
                                   following parent-pointers in parallel */

      do
        {
          low_node_prev = low_node;
          low_node = low_node->parent;

          high_node_prev = high_node;
          high_node = high_node->parent;

          assert (high_node);
          assert (low_node);
        }
      while (high_node != low_node);
      assert (high_node);

      reset_changed_lca_object (nenofex);

      /* must have had at least 2 children, hence capacity greater than 2 */
      assert (changed_subformula->size_children > 2);

#ifndef NDEBUG
      unsigned int old_size = changed_subformula->size_children;
#endif

      changed_subformula->lca = high_node;

      low_node_prev->changed_ch_list_pos = changed_subformula->top_p;
      add_lca_child (nenofex, changed_subformula, low_node_prev);

      high_node_prev->changed_ch_list_pos = changed_subformula->top_p;
      add_lca_child (nenofex, changed_subformula, high_node_prev);

#ifndef NDEBUG
      /* 'realloc' must not have been called */
      assert (old_size == changed_subformula->size_children);
#endif
    }                           /* end: compute 'lca(changed_cur, changed_new)' */

  assert (changed_subformula->num_children <
          changed_subformula->size_children);

  assert (changed_subformula->num_children >= 2);
  assert (changed_subformula->top_p ==
          changed_subformula->children + changed_subformula->num_children);

#ifndef NDEBUG
#if ASSERT_POS_IN_CHANGED_CH_LIST
  assert_pos_in_changed_ch_list (nenofex);
#endif
#endif

  assert (!is_literal_node (nenofex->changed_subformula.lca));
}


#define assign_or_update_changed_subformula(lca_object_p) \
  if (!nenofex->changed_subformula.lca && !is_literal_node((lca_object_p)->lca)) \
    assign_changed_subformula(nenofex, (lca_object_p)); \
  else if (nenofex->changed_subformula.lca) \
    update_changed_subformula(nenofex, (lca_object_p)); \


#ifndef NDEBUG
static void assert_all_subformula_sizes (Nenofex * nenofex);
#endif


/* ---------- START: POST-EXPANSION FLATTENING ---------- */

#define DISTRIBUTIVITY_VAR_POS_MARK 1
#define DISTRIBUTIVITY_VAR_NEG_MARK 2
#define distributivity_var_marked(var) ((var)->simp_mark)
#define distributivity_var_unmark(var) ((var)->simp_mark = 0)
#define distributivity_var_pos_marked(var) ((var)->simp_mark == SIMPLIFY_VAR_POS_MARK)
#define distributivity_var_neg_marked(var) ((var)->simp_mark == SIMPLIFY_VAR_NEG_MARK)
#define distributivity_var_pos_mark(var) ((var)->simp_mark = SIMPLIFY_VAR_POS_MARK)
#define distributivity_var_neg_mark(var) ((var)->simp_mark = SIMPLIFY_VAR_NEG_MARK)

/*
- like resolution (but resolution variable which connects clauses is already gone)
- multiply out clauses
- trivial clauses and double literals will be discarded
- ACTUALLY: not only clauses but graphs are possible as well
*/
Node *
apply_distributivity_of_or_over_and (Nenofex * nenofex, Node * node1,
                                     Node * node2)
{
  assert (!nenofex->distributivity_deleting_redundancies);
  /* flag is used during deletion in order to indicate that 'loose' nodes are deleted */
  nenofex->distributivity_deleting_redundancies = 1;

  Node *result_or;
  Node *copy;

  if (is_literal_node (node1) && is_literal_node (node2))
    {                           /* special case */
      Lit *lit1 = node1->lit;
      Lit *lit2 = node2->lit;
      assert (!distributivity_var_marked (lit1->var));
      assert (!distributivity_var_marked (lit2->var));

      if (lit1->var == lit2->var)
        {                       /* avoid adding redundant nodes */
          if ((lit1->negated && !lit2->negated) ||
              (lit2->negated && !lit1->negated))
            {                   /* will get trivial clause */
              result_or = 0;
            }
          else                  /* will get double literals */
            {
              result_or = copy_formula (nenofex, node1);
            }
        }
      else                      /* different variables -> add both to new OR */
        {
          result_or = or_node (nenofex);
          result_or->size_subformula = 1;

          copy = copy_formula (nenofex, node1);
          add_node_to_child_list (nenofex, result_or, copy);
          result_or->size_subformula += copy->size_subformula;

          copy = copy_formula (nenofex, node2);
          add_node_to_child_list (nenofex, result_or, copy);
          result_or->size_subformula += copy->size_subformula;
        }
    }                           /* end: both are literals */
  else                          /* at least one OR */
    {
      result_or = or_node (nenofex);
      result_or->size_subformula = 1;

      if (is_literal_node (node2))
        {
          Node *tmp = node1;
          node1 = node2;
          node2 = tmp;
        }
      assert (is_or_node (node2));

      if (is_literal_node (node1))
        {
          copy = copy_formula (nenofex, node1);
          add_node_to_child_list (nenofex, result_or, copy);
          result_or->size_subformula += copy->size_subformula;

          Lit *lit = node1->lit;
          assert (!distributivity_var_marked (lit->var));
          if (!lit->negated)
            distributivity_var_pos_mark (lit->var);
          else
            distributivity_var_neg_mark (lit->var);
        }
      else                      /* both node1 and node2 are or */
        {
          assert (is_or_node (node1));
          Node *child1;
          for (child1 = node1->child_list.first;
               child1; child1 = child1->level_link.next)
            {
              assert (is_literal_node (child1) || is_and_node (child1));
              copy = copy_formula (nenofex, child1);
              add_node_to_child_list (nenofex, result_or, copy);
              result_or->size_subformula += copy->size_subformula;

              if (is_literal_node (child1))
                {
                  Lit *lit = child1->lit;
                  assert (!distributivity_var_marked (lit->var));
                  if (!lit->negated)
                    distributivity_var_pos_mark (lit->var);
                  else
                    distributivity_var_neg_mark (lit->var);
                }
            }                   /* end: for all children of node1 */
        }                       /* end: both node1 and node2 are or */

      /* add children of node2 to result_or; ignore double literals, 
         abort if trivial clause is generated */
      Node *child2;
      for (child2 = node2->child_list.first; child2;
           child2 = child2->level_link.next)
        {                       /* check for redundancies before adding */
          if (is_literal_node (child2))
            {
              Lit *lit = child2->lit;
              Var *var = lit->var;
              if (distributivity_var_neg_marked (var))
                {
                  if (!lit->negated)
                    {           /* trivial clause -> abort */
                      break;
                    }
                }
              else if (distributivity_var_pos_marked (var))
                {
                  if (lit->negated)
                    {           /* trivial clause -> abort */
                      break;
                    }
                }
              else              /* new variable -> add and mark */
                {
                  copy = copy_formula (nenofex, child2);
                  add_node_to_child_list (nenofex, result_or, copy);
                  result_or->size_subformula += copy->size_subformula;

                  assert (!distributivity_var_marked (var));
                  if (!lit->negated)
                    distributivity_var_pos_mark (var);
                  else
                    distributivity_var_neg_mark (var);
                }               /* end: add new literal */
            }
          else                  /* is and */
            {
              assert (is_and_node (child2));
              copy = copy_formula (nenofex, child2);
              add_node_to_child_list (nenofex, result_or, copy);
              result_or->size_subformula += copy->size_subformula;
            }                   /* end: child2 is not a literal */
        }                       /* end: for all children of node2 */

      assert (result_or->num_children != 0);
      assert (result_or->child_list.first);
      assert (result_or->child_list.last);

      /* unmark all variables */
      Node *clean_ch;
      for (clean_ch = result_or->child_list.first;
           clean_ch && is_literal_node (clean_ch);
           clean_ch = clean_ch->level_link.next)
        {
          assert (distributivity_var_marked (clean_ch->lit->var));
          distributivity_var_unmark (clean_ch->lit->var);
        }

      if (result_or->num_children == 1)
        {                       /* special case */
          if (child2)
            {                   /* trivial clause: loop exited early -> clean up */
              Node *single_child = result_or->child_list.first;
              unlink_node (nenofex, result_or->child_list.first);
              assert (!single_child->parent);
              assert (is_literal_node (single_child));
              delete_node (nenofex, result_or);
              result_or = 0;
              /* will unlink literal from occ-list as well */
              remove_and_free_subformula (nenofex, single_child);
            }
          else                  /* return single child as result */
            {                   /* CONJECTURE: this case should never occur */
              Node *single_child = result_or->child_list.first;
              unlink_node (nenofex, result_or->child_list.first);
              assert (is_literal_node (single_child));
              delete_node (nenofex, result_or);
              result_or = single_child;
            }
        }
      else                      /* more than one child -> check if trivial or not */
        {
          if (child2)
            {                   /* trivial clause: loop exited early -> clean up */
              assert (!result_or->parent);
              /* will unlink literals from occ-list as well */
              remove_and_free_subformula (nenofex, result_or);
              result_or = 0;
            }
        }

    }                           /* end: not both are literals */

  nenofex->distributivity_deleting_redundancies = 0;
  return result_or;
}


/* 
- case: 'split-or' has two ANDs 
*/
void
flatten_by_ands_at_split_or (Nenofex * nenofex,
                             LCAObject * changed_subformula_new)
{
  Node *split_or = nenofex->existential_split_or;
  Node *split_or_parent = split_or->parent;

  assert (split_or->parent);
  assert (split_or->num_children == 2);
  assert (is_and_node (split_or->child_list.last));
  assert (is_and_node (split_or->child_list.first));
  assert (split_or->child_list.first->level_link.next ==
          split_or->child_list.last);

  int total_size_added = 0;
  Node *disjunction;            /* partial result when distributing OR over AND */
  Node *first_and_child2 = split_or->child_list.last->child_list.first;

  Node *and_child1, *and_child2;
  for (and_child1 = split_or->child_list.first->child_list.first;
       and_child1; and_child1 = and_child1->level_link.next)
    {
      assert (is_literal_node (and_child1) || is_or_node (and_child1));
      for (and_child2 = first_and_child2;
           and_child2; and_child2 = and_child2->level_link.next)
        {
          assert (is_literal_node (and_child2) || is_or_node (and_child2));
          disjunction =
            apply_distributivity_of_or_over_and (nenofex, and_child1,
                                                 and_child2);

          if (disjunction)
            {
              total_size_added += disjunction->size_subformula;
              add_node_to_child_list (nenofex, split_or_parent, disjunction);
              add_lca_child (nenofex, changed_subformula_new, disjunction);
              update_level (nenofex, disjunction);
            }
        }                       /* end: for all children at second AND */
    }                           /* end: for all children at first AND */

  update_size_subformula (nenofex, split_or_parent, total_size_added);
  assert (!nenofex->distributivity_deleting_redundancies);
  remove_and_free_subformula (nenofex, split_or);
}


/* 
- case: 'split-or' has one AND and at least one literal 
- if exactly one literal 'lit' then 'scratch_node' == 'lit'
- else 'scratch_node' is an new (scratch-) OR-node which contains copies of lits
*/
void
flatten_by_literals_at_split_or (Nenofex * nenofex, Node * scratch_node,
                                 LCAObject * changed_subformula_new)
{
  Node *split_or = nenofex->existential_split_or;
  Node *split_or_parent = split_or->parent;

  assert (split_or->parent);
  assert (is_and_node (split_or->child_list.last));
  assert (!is_and_node (split_or->child_list.first));

  int total_size_added = 0;

  Node *disjunction;            /* partial result when distributing OR over AND */

  Node *and_child;
  for (and_child = split_or->child_list.last->child_list.first;
       and_child; and_child = and_child->level_link.next)
    {
      assert (is_literal_node (and_child) || is_or_node (and_child));
      disjunction =
        apply_distributivity_of_or_over_and (nenofex, scratch_node,
                                             and_child);

      if (disjunction)
        {
          total_size_added += disjunction->size_subformula;
          add_node_to_child_list (nenofex, split_or_parent, disjunction);
          add_lca_child (nenofex, changed_subformula_new, disjunction);
          update_level (nenofex, disjunction);
        }
    }                           /* end: for all children at AND */

  update_size_subformula (nenofex, split_or_parent, total_size_added);
  assert (!nenofex->distributivity_deleting_redundancies);
  remove_and_free_subformula (nenofex, split_or);
}


void
post_expansion_flattening (Nenofex * nenofex,
                           LCAObject * changed_subformula_new)
{
  if (nenofex->options.show_progress_specified)
    fprintf (stderr, "post-expansion flattening\n");

  Node *split_or = nenofex->existential_split_or;
  Node *split_or_first_child = 0;

  if (is_and_node (split_or->child_list.last))
    {
      if (is_and_node ((split_or_first_child = split_or->child_list.first)))
        {
          assert (split_or->num_children == 2);
          nenofex->cnt_post_expansion_flattenings++;
          flatten_by_ands_at_split_or (nenofex, changed_subformula_new);
        }
      else
        {
          /* first is lit-node -> possibly one or more literals 
             at split-or -> combine them in one OR */
          assert (is_literal_node (split_or_first_child));
          Node *scratch = 0;

          if (is_literal_node (split_or_first_child->level_link.next))
            {
              scratch = or_node (nenofex);

              Node *child;
              for (child = split_or_first_child;
                   child && is_literal_node (child);
                   child = child->level_link.next)
                {
                  Node *lit_copy = copy_formula (nenofex, child);
                  add_node_to_child_list (nenofex, scratch, lit_copy);
                }               /* end: for all children */
            }                   /* end: more than one literal */
          else
            {                   /* only one literal at split-or */
              assert (is_and_node (split_or_first_child->level_link.next));
              assert (split_or_first_child->level_link.next ==
                      split_or->child_list.last);
              scratch = split_or_first_child;
            }

          nenofex->cnt_post_expansion_flattenings++;
          flatten_by_literals_at_split_or (nenofex, scratch,
                                           changed_subformula_new);

          if (is_or_node (scratch))
            {
              assert (!nenofex->distributivity_deleting_redundancies);
              nenofex->distributivity_deleting_redundancies = 1;        /* workaround */
              assert (!scratch->parent);
              remove_and_free_subformula (nenofex, scratch);
              nenofex->distributivity_deleting_redundancies = 0;
            }
        }                       /* end: literals at split-or */
    }
#ifndef NDEBUG
  else
    {
      Node *child;
      for (child = split_or->child_list.first;
           child; child = child->level_link.next)
        {
          assert (is_literal_node (child));
        }
    }
#endif /* end: ifndef NDEBUG */

#ifndef NDEBUG
#if ASSERT_POST_EXPANSION_FLATTENING
  assert_all_child_occ_lists_integrity (nenofex);
  assert_all_occ_lists_integrity (nenofex);
  assert_all_subformula_sizes (nenofex);
#endif
#endif
/* TODO: LCA-CH-LIST-OCCS (?) */
}


/*
- called before post-expansion flattening is carried out
- check whether situation at 'split-or' stems from an expansion on a CNF-like graph
- if not then do not flatten
- ONE REASON IS: it may happen that 'split-or' has more than 2 AND-children 
    after expanded variable has been assigned and propagated
    but flattening works only if there are exactly 2 AND-children or 
    1 AND-child and arbitrarily many literal-children
*/
int
post_expansion_flattening_check_for_cnf_form (Nenofex *nenofex, Node * split_or)
{
  int result = 1;
  const unsigned int level_threshold = split_or->level + 3;

  Stack *stack = create_stack (nenofex->mm, DEFAULT_STACK_SIZE);
  push_stack (nenofex->mm, stack, split_or);

  Node *cur;
  while ((cur = pop_stack (stack)) && result)
    {
      if (!is_literal_node (cur))
        {
          Node *child;
          for (child = cur->child_list.first; child;
               child = child->level_link.next)
            {
              push_stack (nenofex->mm, stack, child);
            }
        }
      else
        {
          /* is literal -> check distance to split-or: 
             may be at most 3 else graph has not CNF-like form */
          if (cur->level > level_threshold)
            result = 0;
        }
    }

  delete_stack (nenofex->mm, stack);

  return result;
}

void
post_expansion_flattening_reset_changed_new (LCAObject *
                                             changed_subformula_new)
{
  /* workaround: manually reset 'changed_subformula_new' */
  Node **ch, *child;
  for (ch = changed_subformula_new->children; (child = *ch); ch++)
    {
      *ch = 0;
    }
  changed_subformula_new->num_children = 0;
  changed_subformula_new->top_p = changed_subformula_new->children;
  changed_subformula_new->lca = 0;
}

/* ---------- END: POST-EXPANSION FLATTENING ---------- */


/*
- core function: expand an existential variable
- depends on LCA of expanded variable and  LCA-children, a subgraph is copied
- expanded variable will be set to false/true in original/copied subgraph
- graph properties need to be maintained during copying (size, level)
- need to maintain 'changed-subformula'
- NON-INCREASING EXPANSION: possible if LCA(var) has an occurrence of 'var' as 
    child (need not copy, can propagate immediately)
*/
static void
expand_existential_variable (Nenofex * nenofex, Var * var)
{
  assert (var);
  assert (is_existential_scope (var->scope));
  assert (!nenofex->cur_expanded_var);
  assert (!nenofex->existential_split_or);
  assert (var->scope == *nenofex->cur_scope
          || var->scope == *nenofex->next_scope);
  assert (variable_has_occs (var));

  nenofex->cur_expanded_var = var;
  LCAObject *lca_object = &var->exp_costs.lca_object;
  Node *lca_object_lca = lca_object->lca;

  LCAObject changed_subformula_new;
  init_lca_object (nenofex, &changed_subformula_new);

  assert (lca_object_lca);
  assert (lca_object->num_children != 0 || is_literal_node (lca_object_lca));
  assert (!is_literal_node (lca_object_lca) || lca_object->num_children == 0);

  /* flags for revised expansion */
  Node *contained_lit = lca_children_contain_lit (var, lca_object);
  assert (!contained_lit || contained_lit->lit->var == var);
  Node *preemptive_occ = 0;

#if COMPUTE_NUM_NON_INC_EXPANSIONS
  if (contained_lit)
    nenofex->stats.num_non_inc_expansions++;
#endif

  /* used in for post-expansion flattening */
  int set_existential_split_or = 0;
  if (nenofex->options.post_expansion_flattening_specified && ((var->lits[0].
                                                                occ_cnt == 1)
                                                               || (var->
                                                                   lits[1].
                                                                   occ_cnt ==
                                                                   1)
                                                               || (var->
                                                                   lits[0].
                                                                   occ_cnt ==
                                                                   2
                                                                   && var->
                                                                   lits[1].
                                                                   occ_cnt ==
                                                                   2) || (0
                                                                          &&
                                                                          var->
                                                                          lits
                                                                          [0].
                                                                          occ_cnt
                                                                          *
                                                                          var->
                                                                          lits
                                                                          [1].
                                                                          occ_cnt
                                                                          <
                                                                          25)))
    {
      set_existential_split_or = 1;
    }

#ifndef NDEBUG
#if ASSERT_SIZES_IN_EXPANSION
  unsigned int size_before_exp =
    subformula_size (nenofex, nenofex->graph_root);
  unsigned int inc_score = var->exp_costs.inc_score;
  unsigned int dec_score = var->exp_costs.dec_score;
  int check_size = size_before_exp + inc_score - dec_score;
  assert (check_size >= 0);
#endif
#endif

  unsigned int num_children = lca_object_lca->num_children;
  NodeType type = lca_object_lca->type;
  int update_size_delta = 0;

  if (num_children == lca_object->num_children)
    {                           /* CASE 1 */
      if (type == NODE_TYPE_OR)
        {                       /* CASE 1.1 */

#if COMPUTE_CASES_IN_EXPANSIONS
          nenofex->stats.num_exp_case_E_OR_ALL++;
#endif

          if (!contained_lit)
            {
              changed_subformula_new.lca = lca_object_lca;

              /* append copy of children */
              Node **ch, *child;
              for (ch = lca_object->children; (child = *ch); ch++)
                {
                  Node *copy =
                    copy_formula_mark_propagation (nenofex, child, var);

                  add_lca_child (nenofex, &changed_subformula_new, child);
                  add_lca_child (nenofex, &changed_subformula_new, copy);

                  add_node_to_child_list (nenofex, lca_object_lca, copy);
                  update_size_delta += copy->size_subformula;

                  assert (!is_literal_node ((child))
                          || (child)->lit->var == var);
                }
              assert (2 * num_children == lca_object_lca->num_children);

              update_size_subformula (nenofex, lca_object_lca,
                                      update_size_delta);

              assign_or_update_changed_subformula (&changed_subformula_new);

            }                   /* end: relevant children do not contain lit */
          else
            {                   /* propagate that literal preemptively -> will delete parent */
              preemptive_occ = contained_lit;

              assign_or_update_changed_subformula (lca_object);
            }
        }
      else if (type == NODE_TYPE_AND)
        {                       /* CASE 1.2 */

#if COMPUTE_CASES_IN_EXPANSIONS
          nenofex->stats.num_exp_case_E_AND_ALL++;
#endif

          if (contained_lit)
            {
              if (!contained_lit->lit->negated) /* TODO: remove branch, pass flag */
                mark_occs_propagation_var_cost_update (nenofex, var, 1);
              else
                mark_occs_propagation_var_cost_update (nenofex, var, 0);

              assign_or_update_changed_subformula (lca_object);
            }
          else if (lca_object_lca == nenofex->graph_root)
            {
              Node *split_or = or_node (nenofex);

              changed_subformula_new.lca = split_or;

              nenofex->graph_root = split_or;
              add_node_to_child_list (nenofex, split_or, lca_object_lca);
              update_level (nenofex, lca_object_lca);   /* NOTE: merge copy / update-level? */
              Node *copy =
                copy_formula_mark_propagation (nenofex, lca_object_lca, var);
              add_node_to_child_list (nenofex, split_or, copy);

              add_lca_child (nenofex, &changed_subformula_new, lca_object_lca);
              add_lca_child (nenofex, &changed_subformula_new, copy);

              nenofex->graph_root->size_subformula =
                1 + 2 * lca_object_lca->size_subformula;

              assign_or_update_changed_subformula (&changed_subformula_new);
            }
          else                  /* average case */
            {
              assert (lca_object_lca->parent);
              assert (is_or_node (lca_object_lca->parent));

              changed_subformula_new.lca = lca_object_lca->parent;

              Node *copy =
                copy_formula_mark_propagation (nenofex, lca_object_lca, var);

              add_lca_child (nenofex, &changed_subformula_new, lca_object_lca);
              add_lca_child (nenofex, &changed_subformula_new, copy);

              add_node_to_child_list (nenofex, lca_object_lca->parent, copy);

              update_size_subformula (nenofex, lca_object_lca->parent,
                                      lca_object_lca->size_subformula);

              assert (!is_literal_node (copy));

              assign_or_update_changed_subformula (&changed_subformula_new);
            }
        }
      else                      /* type == NODE_TYPE_LITERAL */
        {                       /* CONJECTURE: should not occur if all unates are fully eliminated */
          assert (!lca_object_lca->occ_link.prev);      /* only 1 occ */
          assert (!lca_object_lca->occ_link.next);

          if (!lca_object_lca->parent)
            {
              if (!lca_object_lca->lit->negated)
                truth_propagation_mark (lca_object_lca);
            }
          else if (is_or_node (lca_object_lca->parent))
            {
              if (!lca_object_lca->lit->negated)
                truth_propagation_mark (lca_object_lca);
            }
          else                  /* AND */
            {
              assert (is_and_node (lca_object_lca->parent));

              if (!lca_object_lca->lit->negated)
                truth_propagation_mark (lca_object_lca);
            }

          assign_or_update_changed_subformula (lca_object);
        }
    }
  else
    {                           /* CASE 2: not all children of LCA need to be copied, only relevant ones */
      if (type == NODE_TYPE_OR)
        {                       /* CASE 2.1 */

#if COMPUTE_CASES_IN_EXPANSIONS
          nenofex->stats.num_exp_case_E_OR_SUBSET++;
#endif

          if (!contained_lit)
            {
              changed_subformula_new.lca = lca_object_lca;

              /* append copy of children */
              Node **ch, *child;
              for (ch = lca_object->children; (child = *ch); ch++)
                {
                  Node *copy =
                    copy_formula_mark_propagation (nenofex, child, var);
                  add_node_to_child_list (nenofex, lca_object_lca, copy);
                  assert (!is_literal_node ((child))
                          || (child)->lit->var == var);
                  update_size_delta += copy->size_subformula;

                  add_lca_child (nenofex, &changed_subformula_new, child);
                  add_lca_child (nenofex, &changed_subformula_new, copy);
                }

              assert (num_children + lca_object->num_children ==
                      lca_object_lca->num_children);

              update_size_subformula (nenofex, lca_object_lca,
                                      update_size_delta);

              assign_or_update_changed_subformula (&changed_subformula_new);
            }
          else
            {
              preemptive_occ = contained_lit;

              assign_or_update_changed_subformula (lca_object);
            }
        }
      else if (type == NODE_TYPE_AND)
        {                       /* CASE 2.2 */

#if COMPUTE_CASES_IN_EXPANSIONS
          nenofex->stats.num_exp_case_E_AND_SUBSET++;
#endif

          if (contained_lit)
            {
              if (!contained_lit->lit->negated) /* TODO: remove branch, pass flag */
                mark_occs_propagation_var_cost_update (nenofex, var, 1);
              else
                mark_occs_propagation_var_cost_update (nenofex, var, 0);

              assign_or_update_changed_subformula (lca_object);
            }
          else
            {
              Node *split_or = or_node (nenofex);

              if (set_existential_split_or)
                nenofex->existential_split_or = split_or;

              changed_subformula_new.lca = split_or;

              split_or->size_subformula = 1;
              add_node_to_child_list (nenofex, lca_object_lca, split_or);
              assert (split_or->level == lca_object_lca->level + 1);

              Node *new_and = and_node (nenofex);
              new_and->size_subformula = 1;
              add_node_to_child_list (nenofex, split_or, new_and);
              assert (new_and->level == split_or->level + 1);

              /* BUG - FIX */
              LCAObject *changed_subformula = &(nenofex->changed_subformula);
              unsigned int num_changed_ch_before_relinking =
                changed_subformula->num_children;
              assert (!changed_subformula->lca
                      || changed_subformula->num_children >= 2);

              Node **ch, *child;
              for (ch = lca_object->children; (child = *ch); ch++)
                {
                  unlink_node (nenofex, child);

                  /* BUG - FIX */
                  if (changed_subformula->lca == lca_object_lca
                      && child->changed_ch_list_pos)
                    remove_changed_lca_child (nenofex, child);

                  add_node_to_child_list (nenofex, new_and, child);
                  new_and->size_subformula += (child)->size_subformula;

#ifndef NDEBUG
                  if (is_literal_node ((child)))
                    {
                      assert ((child)->occ_link.next ||
                              (child)->occ_link.prev
                              || (child) == (child)->lit->occ_list.first);
                    }
#endif
                }               /* end: for */

              /* BUG - FIX */
              if (changed_subformula->lca == lca_object_lca)
                {
                  if (changed_subformula->num_children == 0)
                    reset_changed_lca_object (nenofex);
                  else if (changed_subformula->num_children !=
                           num_changed_ch_before_relinking)
                    add_changed_lca_child (nenofex, split_or);

#ifndef NDEBUG
#if ASSERT_POS_IN_CHANGED_CH_LIST
                  assert_pos_in_changed_ch_list (nenofex);
#endif
#endif
                  assert (!changed_subformula->lca ||
                          changed_subformula->num_children >= 2);
                  assert (!changed_subformula->lca ||
                          changed_subformula->top_p ==
                          changed_subformula->children +
                          changed_subformula->num_children);
                }

              update_level (nenofex, new_and);  /* NOTE: merge copy / update level ? */

              Node *copy_and = copy_formula_mark_propagation (nenofex, new_and, var);   /* levels copied */
              add_node_to_child_list (nenofex, split_or, copy_and);

              add_lca_child (nenofex, &changed_subformula_new, new_and);
              add_lca_child (nenofex, &changed_subformula_new, copy_and);

              split_or->size_subformula += 2 * copy_and->size_subformula;
              update_size_subformula (nenofex, split_or->parent,
                                      1 + copy_and->size_subformula + 1);

              if (!set_existential_split_or ||
                  !post_expansion_flattening_check_for_cnf_form (nenofex, nenofex->
                                                                 existential_split_or))
                {
                  nenofex->existential_split_or = 0;
                  assign_or_update_changed_subformula
                    (&changed_subformula_new);
                }
              else
                {
                  assert (nenofex->existential_split_or);
                }
            }
        }
      else
        {
          assert (0);
        }
    }

#ifndef NDEBUG
#if ASSERT_GRAPH_AFTER_EXP_BEFORE_PROP
  assert_expand_graph_integrity (nenofex);
  assert_all_subformula_sizes (nenofex);
#endif
#endif

#ifndef NDEBUG
#if ASSERT_SIZES_IN_EXPANSION
  unsigned int size_after_exp_before_prop =
    subformula_size (nenofex, nenofex->graph_root);
  assert (size_before_exp + inc_score == size_after_exp_before_prop ||
          (((int) (size_before_exp + inc_score - size_after_exp_before_prop)
            >= 0)
           && (size_before_exp + inc_score - size_after_exp_before_prop <=
               2)));
  /* inc_score expected to be EXACT but found pessimistic (->ignore) off-by-one/two errors */
#endif
#endif

  assert (!nenofex->atpg_rr_called);

  if (!preemptive_occ)
    propagate_literals (nenofex, var);  /* graph should be fully reduced and cleaned up */
  else
    {
      assert (contained_lit == preemptive_occ);
      assert (preemptive_occ->parent);
      assert (is_or_node (preemptive_occ->parent));
      propagate_truth (nenofex, preemptive_occ);
    }

#ifndef NDEBUG
#if ASSERT_SIZES_IN_EXPANSION
  unsigned int size_after_exp_after_prop =
    subformula_size (nenofex, nenofex->graph_root);
  int estimated_size = size_before_exp + inc_score - dec_score;
  assert ((int) size_after_exp_after_prop <= estimated_size);   /* upper bound */
#if PRINT_SIZE_CHECK_INFO
  fprintf (stderr, "\tDeviation - Actual size vs. estimated size: %d\n",
           estimated_size - (int) size_after_exp_after_prop);
  fprintf (stderr, "\tActual costs: %d\n\n",
           (size_after_exp_before_prop - size_before_exp) -
           (size_after_exp_before_prop - size_after_exp_after_prop));
#endif
  assert (size_after_exp_after_prop ==
          size_before_exp + (size_after_exp_before_prop - size_before_exp) -
          (size_after_exp_before_prop - size_after_exp_after_prop));
#endif
#endif

  var->eliminated = 1;
  assert (!variable_has_occs (var));

  if (lca_object->lca)
    {
      unlink_variable_from_lca_list (var);
      reset_lca_object (nenofex, var, lca_object, 1);
    }

#ifndef NDEBUG
#if ASSERT_GRAPH_AFTER_EXP_AFTER_PROP
  assert_all_child_occ_lists_integrity (nenofex);
  assert_all_occ_lists_integrity (nenofex);
  assert_all_subformula_sizes (nenofex);
#endif
#endif

  /* post-expansion flattening: 'split-or' node might also 
     have been deleted (and hence reset) during propagations */
  if (nenofex->existential_split_or)
    {
      assert (post_expansion_flattening_check_for_cnf_form
              (nenofex, nenofex->existential_split_or));
      assert (nenofex->options.post_expansion_flattening_specified);

      post_expansion_flattening_reset_changed_new (&changed_subformula_new);
      changed_subformula_new.lca = nenofex->existential_split_or->parent;

      post_expansion_flattening (nenofex, &changed_subformula_new);

      if (changed_subformula_new.num_children == 0)
        {
          post_expansion_flattening_reset_changed_new
            (&changed_subformula_new);
        }
      else if (changed_subformula_new.num_children == 1)
        {
          Node *remaining_child = changed_subformula_new.children[0];
          assert (remaining_child);
          post_expansion_flattening_reset_changed_new
            (&changed_subformula_new);
          if (!is_literal_node (remaining_child))
            {
              changed_subformula_new.lca = remaining_child;
              Node *child;
              for (child = remaining_child->child_list.first;
                   child; child = child->level_link.next)
                {
                  add_lca_child (nenofex, &changed_subformula_new, child);
                }
              assign_or_update_changed_subformula (&changed_subformula_new);
            }
        }
      else
        {
          assign_or_update_changed_subformula (&changed_subformula_new);
        }

      nenofex->existential_split_or = 0;
    }

  nenofex->cur_expanded_var = 0;
  free_lca_children (nenofex, &changed_subformula_new);
  assert (!nenofex->existential_split_or);
}


#ifndef NDEBUG
static void
assert_all_depending_vars_cleaned_up (Nenofex * nenofex)
{
  void **v_scope, **scope_end;
  scope_end = nenofex->scopes->top;
  for (v_scope = nenofex->scopes->elems; v_scope < scope_end; v_scope++)
    {
      Scope *scope = *v_scope;

      void **v_var, **var_end;
      var_end = scope->vars->top;
      for (v_var = scope->vars->elems; v_var < var_end; v_var++)
        {
          Var *var = *v_var;
          assert (!var->collected_as_depending);
          assert (!var->copied);
        }                       /* end: for all vars */

    }                           /* end: for all scopes */
}
#endif


/*
- very similar to 'expand_existential_variable'
*/
static void
expand_universal_variable (Nenofex * nenofex, Var * var)
{
  assert (var);
  assert (is_universal_scope (var->scope));
  assert (!nenofex->cur_expanded_var);
  assert (!nenofex->existential_split_or);
  assert (variable_has_occs (var));

  nenofex->cur_expanded_var = var;
  LCAObject *lca_object = &var->exp_costs.lca_object;
  Node *lca_object_lca = lca_object->lca;

  LCAObject changed_subformula_new;
  init_lca_object (nenofex, &changed_subformula_new);

  assert (lca_object_lca);
  assert (lca_object->num_children != 0 || is_literal_node (lca_object_lca));
  assert (!is_literal_node (lca_object_lca) || lca_object->num_children == 0);

  /* flags for revised expansion */
  Node *contained_lit = lca_children_contain_lit (var, lca_object);
  assert (!contained_lit || contained_lit->lit->var == var);
  Node *preemptive_occ = 0;

#ifndef NDEBUG
#if ASSERT_SIZES_IN_EXPANSION
  unsigned int size_before_exp =
    subformula_size (nenofex, nenofex->graph_root);
  unsigned int inc_score = var->exp_costs.inc_score;
  unsigned int dec_score = var->exp_costs.dec_score;
  int check_size = size_before_exp + inc_score - dec_score;
  assert (check_size >= 0);
#endif
#endif

  unsigned int num_children = lca_object_lca->num_children;
  NodeType type = lca_object_lca->type;
  int update_size_delta = 0;

  if (num_children == lca_object->num_children)
    {                           /* CASE 1 */
      if (type == NODE_TYPE_AND)
        {                       /* CASE 1.1 */

#if COMPUTE_CASES_IN_EXPANSIONS
          nenofex->stats.num_exp_case_A_AND_ALL++;
#endif

          /* append copy of children */
          if (!contained_lit)
            {
              changed_subformula_new.lca = lca_object_lca;

              Node **ch, *child;
              for (ch = lca_object->children; (child = *ch); ch++)
                {
                  Node *copy =
                    copy_formula_mark_propagation (nenofex, child, var);
                  add_node_to_child_list (nenofex, lca_object_lca, copy);
                  update_size_delta += copy->size_subformula;
                  assert (!is_literal_node ((child))
                          || (child)->lit->var != var);

                  add_lca_child (nenofex, &changed_subformula_new, child);
                  add_lca_child (nenofex, &changed_subformula_new, copy);
                }
              assert (2 * num_children == lca_object_lca->num_children);
              update_size_subformula (nenofex, lca_object_lca,
                                      update_size_delta);

              assign_or_update_changed_subformula (&changed_subformula_new);
            }
          else
            {
              preemptive_occ = contained_lit;

              assign_or_update_changed_subformula (lca_object);
            }
        }
      else if (type == NODE_TYPE_OR)
        {                       /* CASE 1.2 */

#if COMPUTE_CASES_IN_EXPANSIONS
          nenofex->stats.num_exp_case_A_OR_ALL++;
#endif

          if (contained_lit)
            {
              if (!contained_lit->lit->negated) /* TODO: remove branch, pass flag */
                mark_occs_propagation_var_cost_update (nenofex, var, 0);
              else
                mark_occs_propagation_var_cost_update (nenofex, var, 1);

              assign_or_update_changed_subformula (lca_object);
            }
          else if (lca_object_lca == nenofex->graph_root)
            {
              Node *split_and = and_node (nenofex);

              changed_subformula_new.lca = split_and;

              nenofex->graph_root = split_and;
              add_node_to_child_list (nenofex, split_and, lca_object_lca);
              update_level (nenofex, lca_object_lca);   /* TODO: merge copy / update_level */
              Node *copy =
                copy_formula_mark_propagation (nenofex, lca_object_lca, var);
              add_node_to_child_list (nenofex, split_and, copy);

              add_lca_child (nenofex, &changed_subformula_new, lca_object_lca);
              add_lca_child (nenofex, &changed_subformula_new, copy);

              nenofex->graph_root->size_subformula =
                1 + 2 * lca_object_lca->size_subformula;

              assign_or_update_changed_subformula (&changed_subformula_new);
            }
          else                  /* average case */
            {
              assert (lca_object_lca->parent);
              assert (is_and_node (lca_object_lca->parent));

              changed_subformula_new.lca = lca_object_lca->parent;

              Node *copy =
                copy_formula_mark_propagation (nenofex, lca_object_lca, var);

              add_lca_child (nenofex, &changed_subformula_new, lca_object_lca);
              add_lca_child (nenofex, &changed_subformula_new, copy);

              add_node_to_child_list (nenofex, lca_object_lca->parent, copy);

              update_size_subformula (nenofex, lca_object_lca->parent,
                                      lca_object_lca->size_subformula);

              assert (!is_literal_node (copy));

              assign_or_update_changed_subformula (&changed_subformula_new);
            }
        }
      else                      /* type == NODE_TYPE_LITERAL */
        {                       /* CONJECTURE: should not occur if all unates are fully eiminated */
          assert (!lca_object_lca->occ_link.next);      /* only 1 occ */
          assert (!lca_object_lca->occ_link.prev);

          if (!lca_object_lca->parent)
            {
              if (lca_object_lca->lit->negated)
                truth_propagation_mark (lca_object_lca);
            }
          else if (is_and_node (lca_object_lca->parent))
            {
              if (lca_object_lca->lit->negated)
                truth_propagation_mark (lca_object_lca);
            }
          else                  /* OR */
            {
              assert (is_or_node (lca_object_lca->parent));

              if (lca_object_lca->lit->negated)
                truth_propagation_mark (lca_object_lca);
            }

          assign_or_update_changed_subformula (lca_object);
        }
    }
  else
    {                           /* CASE 2: not all children of LCA need to be copied, only relevant ones */
      if (type == NODE_TYPE_AND)
        {                       /* CASE 2.1 */

#if COMPUTE_CASES_IN_EXPANSIONS
          nenofex->stats.num_exp_case_A_AND_SUBSET++;
#endif

          if (!contained_lit)
            {
              changed_subformula_new.lca = lca_object_lca;

              /* append copy of children */
              Node **ch, *child;
              for (ch = lca_object->children; (child = *ch); ch++)
                {
                  Node *copy =
                    copy_formula_mark_propagation (nenofex, child, var);
                  add_node_to_child_list (nenofex, lca_object_lca, copy);
                  update_size_delta += copy->size_subformula;
                  assert (!is_literal_node ((child))
                          || (child)->lit->var != var);

                  add_lca_child (nenofex, &changed_subformula_new, child);
                  add_lca_child (nenofex, &changed_subformula_new, copy);
                }
              assert (num_children + lca_object->num_children ==
                      lca_object_lca->num_children);
              update_size_subformula (nenofex, lca_object_lca,
                                      update_size_delta);

              assign_or_update_changed_subformula (&changed_subformula_new);
            }
          else
            {
              preemptive_occ = contained_lit;

              assign_or_update_changed_subformula (lca_object);
            }
        }
      else if (type == NODE_TYPE_OR)
        {                       /* CASE 2.2 */

#if COMPUTE_CASES_IN_EXPANSIONS
          nenofex->stats.num_exp_case_A_OR_SUBSET++;
#endif

          if (contained_lit)
            {
              if (!contained_lit->lit->negated) /* NOTE: remove branch, pass flag */
                mark_occs_propagation_var_cost_update (nenofex, var, 0);
              else
                mark_occs_propagation_var_cost_update (nenofex, var, 1);

              assign_or_update_changed_subformula (lca_object);
            }
          else
            {
              Node *split_and = and_node (nenofex);

              changed_subformula_new.lca = split_and;

              split_and->size_subformula = 1;
              add_node_to_child_list (nenofex, lca_object_lca, split_and);
              assert (split_and->level == lca_object_lca->level + 1);

              Node *new_or = or_node (nenofex);
              new_or->size_subformula = 1;
              add_node_to_child_list (nenofex, split_and, new_or);
              assert (new_or->level == split_and->level + 1);

              /* BUG - FIX */
              LCAObject *changed_subformula = &(nenofex->changed_subformula);
              unsigned int num_changed_ch_before_relinking =
                changed_subformula->num_children;
              assert (!changed_subformula->lca
                      || changed_subformula->num_children >= 2);

              Node **ch, *child;
              for (ch = lca_object->children; (child = *ch); ch++)
                {
                  unlink_node (nenofex, child);

                  /* BUG - FIX */
                  if (changed_subformula->lca == lca_object_lca
                      && (child)->changed_ch_list_pos)
                    remove_changed_lca_child (nenofex, child);

                  add_node_to_child_list (nenofex, new_or, child);
                  new_or->size_subformula += (child)->size_subformula;

#ifndef NDEBUG
                  if (is_literal_node ((child)))
                    {
                      assert ((child)->occ_link.next ||
                              (child)->occ_link.prev
                              || (child) == (child)->lit->occ_list.first);
                    }
#endif
                }

              /* BUG - FIX */
              if (changed_subformula->lca == lca_object_lca)
                {
                  if (changed_subformula->num_children == 0)
                    reset_changed_lca_object (nenofex);
                  else if (changed_subformula->num_children !=
                           num_changed_ch_before_relinking)
                    add_changed_lca_child (nenofex, split_and);

#ifndef NDEBUG
#if ASSERT_POS_IN_CHANGED_CH_LIST
                  assert_pos_in_changed_ch_list (nenofex);
#endif
#endif
                  assert (!changed_subformula->lca
                          || changed_subformula->num_children >= 2);
                  assert (!changed_subformula->lca
                          || changed_subformula->top_p ==
                          changed_subformula->children +
                          changed_subformula->num_children);
                }

              update_level (nenofex, new_or);   /* NOTE: merge copy / update_level ? */

              Node *copy_or =
                copy_formula_mark_propagation (nenofex, new_or, var);
              add_node_to_child_list (nenofex, split_and, copy_or);

              add_lca_child (nenofex, &changed_subformula_new, new_or);
              add_lca_child (nenofex, &changed_subformula_new, copy_or);

              split_and->size_subformula += 2 * copy_or->size_subformula;
              update_size_subformula (nenofex, split_and->parent,
                                      1 + copy_or->size_subformula + 1);

              assign_or_update_changed_subformula (&changed_subformula_new);
            }
        }
      else
        {
          assert (0);
        }
    }

#ifndef NDEBUG
#if ASSERT_GRAPH_AFTER_EXP_BEFORE_PROP
  assert_expand_graph_integrity (nenofex);
  assert_all_subformula_sizes (nenofex);
#endif
#endif

#ifndef NDEBUG
#if ASSERT_SIZES_IN_EXPANSION
  unsigned int size_after_exp_before_prop =
    subformula_size (nenofex, nenofex->graph_root);
  assert (size_before_exp + inc_score == size_after_exp_before_prop ||
          (((int) (size_before_exp + inc_score - size_after_exp_before_prop)
            >= 0)
           && (size_before_exp + inc_score - size_after_exp_before_prop <=
               2)));
  /* inc_score expected to be EXACT but we found pessimistic (->ignore) off-by-one/two errors */
#endif
#endif

  assert (!nenofex->atpg_rr_called);

  if (!preemptive_occ)
    propagate_literals (nenofex, var);  /* graph should be fully reduced and cleaned up */
  else
    {
      assert (contained_lit == preemptive_occ);
      assert (preemptive_occ->parent);
      assert (is_and_node (preemptive_occ->parent));
      propagate_falsity (nenofex, preemptive_occ);
    }

#ifndef NDEBUG
#if ASSERT_SIZES_IN_EXPANSION
  unsigned int size_after_exp_after_prop =
    subformula_size (nenofex, nenofex->graph_root);
  int estimated_size = size_before_exp + inc_score - dec_score;
  assert ((int) size_after_exp_after_prop <= estimated_size);   /* upper bound */
#if PRINT_SIZE_CHECK_INFO
  fprintf (stderr, "\tDeviation - Actual size vs. estimated size: %d\n",
           estimated_size - (int) size_after_exp_after_prop);
  fprintf (stderr, "\tActual costs: %d\n\n",
           (size_after_exp_before_prop - size_before_exp) -
           (size_after_exp_before_prop - size_after_exp_after_prop));
#endif
  assert (size_after_exp_after_prop == size_before_exp +
          (size_after_exp_before_prop - size_before_exp) -
          (size_after_exp_before_prop - size_after_exp_after_prop));
#endif
#endif

  var->eliminated = 1;
  assert (!variable_has_occs (var));

  if (lca_object->lca)
    {
      unlink_variable_from_lca_list (var);
      reset_lca_object (nenofex, var, lca_object, 1);
    }

#ifndef NDEBUG
#if ASSERT_GRAPH_AFTER_EXP_AFTER_PROP
  assert_all_child_occ_lists_integrity (nenofex);
  assert_all_occ_lists_integrity (nenofex);
  assert_all_subformula_sizes (nenofex);
#endif
#endif

  nenofex->cur_expanded_var = 0;
  free_lca_children (nenofex, &changed_subformula_new);
  assert (!nenofex->existential_split_or);

  if (count_stack (nenofex->depending_vars))
    {                           /* expansion of non-innermost universal variable -> need to clean up dep. vars */
      assert (var->scope == (*nenofex->next_scope));
      assert (is_existential_scope (*nenofex->cur_scope));

      Var *depending_var;
      while ((depending_var = pop_stack (nenofex->depending_vars)))
        {
          assert (is_existential_scope (depending_var->scope));
          assert (depending_var->scope->nesting >
                  (*nenofex->next_scope)->nesting);
          assert (depending_var->collected_as_depending);
          assert (depending_var->copied);

          depending_var->collected_as_depending = 0;
          depending_var->copied = 0;
        }                       /* end while stack not empty */

#ifndef NDEBUG
#if ASSERT_ALL_DEPENDING_VARS_CLEANED_UP
      assert_all_depending_vars_cleaned_up (nenofex);
#endif
#endif
    }                           /* end: clean up depending variables */
}


/* 
- determines number of nodes to be created when expanding variable 'var'
- type of LCA and type of var influence this value (8 cases)
*/
static unsigned int
expansion_increase_score (Nenofex * nenofex, Var * var,
                          LCAObject * lca_object)
{
  assert (lca_object->lca);
  unsigned int inc_score = 0;

#ifndef NDEBUG
  Node **ch_test, *child_test;
  unsigned int test_score = 0;
  for (ch_test = lca_object->children; (child_test = *ch_test); ch_test++)
    {
      test_score++;
      if (is_literal_node ((child_test)))
        assert ((is_universal_scope (var->scope)
                 && var->scope->nesting < (*nenofex->cur_scope)->nesting)
                || (child_test)->lit->var == var);
    }
  assert (test_score == lca_object->num_children);
#endif

  Node *lca = lca_object->lca;
  NodeType lca_type = lca->type;

  assert (!is_literal_node (lca) || !lca_object->children[0]);

  /* special case where LCA-children contain literal (of var to be expanded) */
  if (lca_children_contain_lit (var, lca_object) || is_literal_node (lca))
    {
      assert (inc_score == 0);
#if COMPUTE_NUM_NON_INC_EXPANSIONS_IN_SCORES
      nenofex->stats.num_non_inc_expansions_in_scores++;
#endif
      return inc_score;
    }

  assert (!is_literal_node (lca));

  /* increment 'inc_score' depending on following situations */
  if (is_existential_scope (var->scope))
    {
      if (lca_object->num_children == lca->num_children)        /* copy all */
        {
          if (lca_type == NODE_TYPE_AND)
            {
              inc_score += lca->size_subformula;
              if (lca == nenofex->graph_root)   /* create split-OR in this case */
                inc_score++;
            }
          else                  /* OR */
            {
              assert (lca_type == NODE_TYPE_OR);
              Node **ch, *child;
              for (ch = lca_object->children; (child = *ch); ch++)
                {               /* count subformula-sizes of lca's relevant children */
                  inc_score += (child)->size_subformula;
                }               /* end: for all children */
            }
        }
      else                      /* copy only lca's relevant children */
        {
          if (lca->type == NODE_TYPE_OR)
            {
              Node **ch, *child;
              for (ch = lca_object->children; (child = *ch); ch++)
                {               /* count subformula-sizes of lca's relevant children */
                  inc_score += (child)->size_subformula;
                }               /* end: for all children */
            }
          else if (lca_type == NODE_TYPE_AND)
            {
              /* add split-or and 2 new and-nodes holding copied children of lca */
              Node **ch, *child;
              for (ch = lca_object->children; (child = *ch); ch++)
                {               /* count subformula-sizes of lca's relevant children */
                  inc_score += (child)->size_subformula;
                }               /* end: for all children */
              inc_score += 3;   /* add split-or + two new ANDs */
            }
        }
    }
  else                          /* universal variables */
    {
      if (lca_object->num_children == lca->num_children)        /* copy all */
        {
          if (lca_type == NODE_TYPE_OR)
            {
              inc_score += lca->size_subformula;
              if (lca == nenofex->graph_root)   /* have to create split-AND in this case */
                inc_score++;
            }
          else                  /* AND */
            {
              assert (lca_type == NODE_TYPE_AND);
              Node **ch, *child;
              for (ch = lca_object->children; (child = *ch); ch++)
                {               /* count subformula-sizes of lca's relevant children */
                  inc_score += (child)->size_subformula;
                }               /* end: for all children */
            }
        }
      else                      /* copy only lca's relevant children */
        {
          if (lca->type == NODE_TYPE_AND)
            {
              Node **ch, *child;
              for (ch = lca_object->children; (child = *ch); ch++)
                {               /* count subformula-sizes of lca's relevant children */
                  inc_score += (child)->size_subformula;
                }               /* end: for all children */
            }
          else if (lca_type == NODE_TYPE_OR)
            {
              /* add split-or and 2 new and-nodes holding copied children of lca */
              Node **ch, *child;
              for (ch = lca_object->children; (child = *ch); ch++)
                {               /* count subformula-sizes of lca's relevant children */
                  inc_score += (child)->size_subformula;
                }               /* end: for all children */
              inc_score += 3;   /* add split-and + two new ORs */
            }
        }
    }                           /* end: universal variables */

  return inc_score;
}


/*
- count nodes that will be deleted when setting variable to false
*/
static void
decrease_score_propagate_falsity (Nenofex * nenofex, Node * occ,
                                  LCAObject * lca_object)
{
  assert (occ);
  assert (is_literal_node (occ));

  if (occ == nenofex->graph_root)
    {
      assert (!decrease_score_marked (occ));
      decrease_score_mark (occ);
      return;
    }

  Node *occ_parent = occ->parent;
  assert (occ_parent);

  Node *lca_object_lca = lca_object->lca;

  if (is_and_node (occ_parent))
    {
      if (is_existential_scope (occ->lit->var->scope))
        {
          if (occ_parent == lca_object_lca)
            {
              assert (!decrease_score_marked (occ_parent));
            }
          else if (occ == lca_object_lca)
            {
              assert (is_literal_node (lca_object_lca));
            }
          else
            {
              decrease_score_mark (occ_parent);
            }
        }                       /* end: existential var. */
      else
        {
          decrease_score_mark (occ_parent);
        }
    }
  else                          /* parent is OR */
    {
      decrease_score_mark (occ);
    }
}


/*
- count nodes that will be deleted when setting variable to true
*/
static void
decrease_score_propagate_truth (Nenofex * nenofex, Node * occ,
                                LCAObject * lca_object)
{
  assert (occ);
  assert (is_literal_node (occ));

  if (occ == nenofex->graph_root)
    {
      assert (!decrease_score_marked (occ));
      decrease_score_mark (occ);
      return;
    }

  Node *occ_parent = occ->parent;
  assert (occ_parent);

  Node *lca_object_lca = lca_object->lca;

  if (is_or_node (occ_parent))
    {
      if (is_universal_scope (occ->lit->var->scope))
        {
          if (occ_parent == lca_object_lca)
            {
              assert (!decrease_score_marked (occ_parent));
            }
          else if (occ == lca_object_lca)
            {
              assert (is_literal_node (lca_object_lca));
            }
          else
            {
              decrease_score_mark (occ_parent);
            }
        }                       /* end: universal vars */
      else
        {
          decrease_score_mark (occ_parent);
        }
    }
  else                          /* parent is AND */
    {
      decrease_score_mark (occ);
    }
}


/*
- set variable 'virtually' to true/false and count node decrease
- nodes which have been marked would have been deleted by propagation
- collect and unmark nodes bottom-up
- pessimistic score; might lose more by parent-merging or 1-l-simp
*/
static unsigned int
decrease_score_count_deleted (Nenofex * nenofex, Var * var)
{
  unsigned int num_deleted = 0;

  Lit *lit = var->lits;
  Node *var_lca = var->exp_costs.lca_object.lca;
  assert (var_lca);

  Stack *collected_nodes = create_stack (nenofex->mm, DEFAULT_STACK_SIZE);

  Node *occ;

AGAIN:

  for (occ = lit->occ_list.first; occ; occ = occ->occ_link.next)
    {
      Node *cur, *highest_marked;

      cur = occ;
      assert (is_literal_node (cur));

      if (!decrease_score_marked (cur))
        {
          cur = cur->parent;
          if (!cur)             /* special case: only one occ which is at root */
            {
              assert (0);
            }
          else if (!decrease_score_marked (cur))
            {                   /* parent already unmarked -> there is a collected node on path up to root */
              continue;
            }
        }                       /* end: if occ not marked */
      assert ((is_literal_node (cur) && decrease_score_marked (cur)) ||
              (!is_literal_node (cur) && decrease_score_marked (cur)));

      highest_marked = cur;
      cur = cur->parent;

      unsigned const int lowest_level =
        var_lca->parent ? var_lca->parent->level : var_lca->level;

      int found_collected = 0;
      while (cur && cur->level >= lowest_level) /* NOTE: strengthen loop condition ? */
        {
          assert (!is_literal_node (cur));

          if (decrease_score_marked (cur))
            {
              assert (!decrease_score_collected_marked (cur));
              decrease_score_unmark (highest_marked);
              highest_marked = cur;
            }
          else if (decrease_score_collected_marked (cur))
            {
              found_collected = 1;
              break;
            }

          cur = cur->parent;
        }                       /* end: while */

      if (found_collected)
        {
          decrease_score_unmark (highest_marked);
        }
      else
        {
          decrease_score_unmark (highest_marked);
          assert (!decrease_score_collected_marked (highest_marked));
          decrease_score_collected_mark (highest_marked);
          push_stack (nenofex->mm, collected_nodes, highest_marked);
        }
    }                           /* end: for all occurrences */

  if (lit == var->lits)
    {
      lit++;
      assert (lit == var->lits + 1);
      goto AGAIN;               /* visit positive occurrences */
    }

  Node *collected_node;
  while ((collected_node = pop_stack (collected_nodes)))
    {
      assert (decrease_score_collected_marked (collected_node));
      decrease_score_collected_unmark (collected_node);
      num_deleted += collected_node->size_subformula;
    }                           /* end: while */

  delete_stack (nenofex->mm, collected_nodes);

  return num_deleted;
}


/*
- determine how many nodes will be deleted if expanding var and propagating literals
- TODO: REVISION NECESSARY (cases of non-increasing expansions properly captured?)
*/

#define REVISION 1

static unsigned int
expansion_decrease_score (Nenofex * nenofex, Var * var,
                          LCAObject * lca_object)
{
  unsigned int dec_score = 0;

  Node *occ;
  Lit *lit = var->lits;
  assert (lit->negated);

  Node *contained_lit = lca_children_contain_lit (var, lca_object);
  assert (!contained_lit || contained_lit->lit->var == var);

  assert (!contained_lit || !is_literal_node (lca_object->lca));

  if (contained_lit || is_literal_node (lca_object->lca))
    {

#if !REVISION
      if ((contained_lit && !contained_lit->lit->negated) ||
          (!contained_lit && !lca_object->lca->lit->negated))
        {
          goto TRUTH_PROPAGATION;
        }
#else
      if ((contained_lit && !contained_lit->lit->negated
           && is_existential_scope (var->scope)) || (contained_lit
                                                     && contained_lit->lit->
                                                     negated
                                                     &&
                                                     is_universal_scope (var->
                                                                         scope))
          || (!contained_lit && !lca_object->lca->lit->negated
              && is_existential_scope (var->scope)) || (!contained_lit
                                                        && lca_object->lca->
                                                        lit->negated
                                                        &&
                                                        is_universal_scope
                                                        (var->scope)))
        {
          goto TRUTH_PROPAGATION;
        }
#endif
    }

  /* for all neg. occs: pretend to propagate falsity and count node decrease */
  for (occ = lit->occ_list.first; occ; occ = occ->occ_link.next)
    {
      decrease_score_propagate_truth (nenofex, occ, lca_object);
    }
  lit = var->lits + 1;
  assert (!lit->negated);
  /* similarly for all positve occurrences */
  for (occ = lit->occ_list.first; occ; occ = occ->occ_link.next)
    {
      decrease_score_propagate_falsity (nenofex, occ, lca_object);
    }

  dec_score += decrease_score_count_deleted (nenofex, var);

  if (contained_lit || is_literal_node (lca_object->lca))
    {
#if !REVISION
      if ((contained_lit && contained_lit->lit->negated) ||
          (!contained_lit && lca_object->lca->lit->negated))
        {
          goto FINISHED;
        }
#else
      if ((contained_lit && !contained_lit->lit->negated
           && is_universal_scope (var->scope)) || (contained_lit
                                                   && contained_lit->lit->
                                                   negated
                                                   &&
                                                   is_existential_scope (var->
                                                                         scope))
          || (!contained_lit && !lca_object->lca->lit->negated
              && is_universal_scope (var->scope)) || (!contained_lit
                                                      && lca_object->lca->
                                                      lit->negated
                                                      &&
                                                      is_existential_scope
                                                      (var->scope)))
        {
          goto FINISHED;
        }
#endif
    }

TRUTH_PROPAGATION:

#ifndef NDEBUG
#if ASSERT_GRAPH_BETWEEN_DEC_SCORE
  assert_all_child_occ_lists_integrity (nenofex);
  assert_all_occ_lists_integrity (nenofex);
#endif
#endif

  lit = var->lits;
  /* for all neg. occs: pretend to propagate truth and count node decrease */
  for (occ = lit->occ_list.first; occ; occ = occ->occ_link.next)
    {
      decrease_score_propagate_falsity (nenofex, occ, lca_object);
    }
  lit = var->lits + 1;
  /* similarly for all positve occurrences */
  for (occ = lit->occ_list.first; occ; occ = occ->occ_link.next)
    {
      decrease_score_propagate_truth (nenofex, occ, lca_object);
    }

  dec_score += decrease_score_count_deleted (nenofex, var);

FINISHED:

#ifndef NDEBUG
#if ASSERT_GRAPH_AFTER_DEC_SCORE
  assert_all_child_occ_lists_integrity (nenofex);
  assert_all_occ_lists_integrity (nenofex);
#endif
#endif

  return dec_score;
}


/* 
- compute LCA and scores for variable according to marks set
*/
static void
init_variable_scores (Nenofex * nenofex, Var * var,
                      const int update_key_priority_queue)
{
  if (!variable_has_occs (var))
    {
      return;
    }

  int old_score = var->exp_costs.score;

  /*assert(variable_has_occs(var)); */

  assert (!lca_update_marked (var) ||
          (inc_score_update_marked (var) && dec_score_update_marked (var)));

  if (lca_update_marked (var))
    {
      if (var->exp_costs.lca_object.lca)
        {
          assert (var->exp_costs.lca_object.lca->var_lca_list.first);
          assert (var->exp_costs.lca_object.lca->var_lca_list.last);

          unlink_variable_from_lca_list (var);
          reset_lca_object (nenofex, var, &var->exp_costs.lca_object, 1);
        }

      if (is_universal_scope (var->scope) && nenofex->next_scope &&
          var->scope == *nenofex->next_scope && nenofex->cur_scope &&
          is_existential_scope (*nenofex->cur_scope))
        {
          find_non_innermost_universal_lca_and_children (nenofex, var);
        }
      else
        {
          find_variable_lca_and_children (nenofex, var,
                                          &var->exp_costs.lca_object, 1);
        }

#ifndef NDEBUG
#if ASSERT_INIT_VAR_SCORES_ALL_UNMARKED
      assert_all_lca_children_unmarked (&var->exp_costs.lca_object);
#endif
#endif
    }                           /* end: variable marked for lca update */

  if (inc_score_update_marked (var))
    var->exp_costs.inc_score =
      expansion_increase_score (nenofex, var, &var->exp_costs.lca_object);

  if (dec_score_update_marked (var))
    var->exp_costs.dec_score =
      expansion_decrease_score (nenofex, var, &var->exp_costs.lca_object);

  if (inc_score_update_marked (var) || dec_score_update_marked (var))
    var->exp_costs.score =
      var->exp_costs.inc_score - var->exp_costs.dec_score;

  if (update_key_priority_queue)
    update_key (var->scope->priority_heap, var, old_score);
}


static void
add_lit_node_to_occurrence_list (Nenofex * nenofex, Node * new_occ)
{
  assert (is_literal_node (new_occ));
  assert (new_occ);
  assert (!new_occ->occ_link.next);
  assert (!new_occ->occ_link.prev);

#ifndef NDEBUG
  Lit *lit_p = new_occ->lit;
  assert (lit_p);
  if (lit_p->negated)
    assert (lit_p == lit_p->var->lits);
  else
    assert (lit_p == lit_p->var->lits + 1);
#endif

  Lit *lit = new_occ->lit;
  assert (lit);

  if (!lit->occ_list.first)
    {                           /* first occurrence */
      assert (!lit->occ_list.last);

      lit->occ_list.first = lit->occ_list.last = new_occ;
    }
  else
    {                           /* append */
      assert (lit->occ_list.last);

      lit->occ_list.last->occ_link.next = new_occ;
      new_occ->occ_link.prev = lit->occ_list.last;
      lit->occ_list.last = new_occ;

      assert (!new_occ->occ_link.next);
    }

  lit->occ_cnt++;

  assert (new_occ->occ_link.next || new_occ->lit->occ_list.last == new_occ);
  assert (new_occ->occ_link.prev || new_occ->lit->occ_list.first == new_occ);
}


static void
add_node_to_child_list_before (Nenofex * nenofex, Node * child,
                               Node * new_child);


/*
- introduced convention that literals are stored first in child list
*/
static void
add_lit_node_to_child_list (Nenofex * nenofex, Node * parent,
                            Node * lit_child)
{
  assert (parent->child_list.first);
  assert (parent->child_list.last);
  assert (parent->num_children >= 1);
  assert (is_literal_node (lit_child));

  add_node_to_child_list_before (nenofex, parent->child_list.first,
                                 lit_child);
}


void
add_node_to_child_list (Nenofex * nenofex, Node * parent, Node * new_child)
{
  assert (parent);
  assert (new_child);
  assert (!new_child->level_link.next);
  assert (!new_child->level_link.prev);
  assert (!is_literal_node (parent));

  /* introduced convention that literals are stored first in child list */
  if (is_literal_node (new_child) && parent->child_list.first)
    {                           /* parent has at least 1 child */
      add_lit_node_to_child_list (nenofex, parent, new_child);
      return;
    }

  if (!parent->child_list.first)
    {                           /* 'new_child' is the first child in list */
      assert (!parent->child_list.last);

      parent->child_list.first = parent->child_list.last = new_child;
      new_child->parent = parent;
      new_child->level = parent->level + 1;
      parent->num_children++;
    }
  else
    {                           /* append 'new_child' to list */
      assert (parent->child_list.last);
      assert (!parent->child_list.last->level_link.next);

      parent->child_list.last->level_link.next = new_child;
      new_child->level_link.prev = parent->child_list.last;
      parent->child_list.last = new_child;
      new_child->parent = parent;
      new_child->level = parent->level + 1;
      parent->num_children++;
    }

  assert (new_child->level == parent->level + 1);
  assert (!new_child->level_link.next);
}


/* inserts 'new_child' before 'child' in child list */
static void
add_node_to_child_list_before (Nenofex * nenofex, Node * child,
                               Node * new_child)
{
  Node *parent = child->parent;

  assert (child);
  assert (parent);
  assert (new_child);
  assert (!new_child->level_link.next);
  assert (!new_child->level_link.prev);
  assert (!is_literal_node (parent));

  if (!parent->child_list.first)
    {                           /* 'new_child' is the first child in list */
      assert (!parent->child_list.last);

      parent->child_list.first = parent->child_list.last = new_child;
      new_child->parent = parent;
      new_child->level = parent->level + 1;

      assert (!new_child->level_link.next);
    }
  else
    {                           /* insert 'new_child' to list */
      assert (parent->child_list.last);
      assert (!parent->child_list.last->level_link.next);

      new_child->level_link.next = child;
      new_child->level_link.prev = child->level_link.prev;
      child->level_link.prev = new_child;

      if (new_child->level_link.prev)
        {                       /* standard case */
          assert (child != parent->child_list.first);

          new_child->level_link.prev->level_link.next = new_child;
        }
      else
        {                       /* prepending */
          assert (child == parent->child_list.first);

          parent->child_list.first = new_child;
        }

      new_child->parent = parent;
      new_child->level = parent->level + 1;
    }
  parent->num_children++;

  assert (new_child->level == parent->level + 1);
}

static void
add_orig_clause_aux (Nenofex * nenofex, Node *clause)
{
  /* first two clauses are not simplified after parsing 
     because this could delete whole graph */
  if (nenofex->num_added_clauses == 1)
    {
      assert (nenofex->graph_root->num_children == 1);
      assert (!nenofex->first_added_clause);
      nenofex->first_added_clause = clause;
    }
  else if (nenofex->num_added_clauses == 2)
    {
      assert (nenofex->graph_root->num_children == 2);
      assert (!nenofex->second_added_clause);
      nenofex->second_added_clause = clause;
    }
}


static void
delete_scope (Nenofex * nenofex, Scope * scope)
{
  delete_stack (nenofex->mm, scope->vars);
  delete_priority_queue (nenofex->mm, &scope->priority_heap);
  mem_free (nenofex->mm, scope, sizeof (Scope));
}


static Scope *
new_scope (Nenofex * nenofex)
{
  size_t bytes = sizeof (Scope);
  Scope *result = (Scope *) mem_malloc (nenofex->mm, bytes);
  assert (result);
  memset (result, 0, bytes);

  result->vars = create_stack (nenofex->mm, DEFAULT_STACK_SIZE);
  create_priority_queue (nenofex->mm, &result->priority_heap, DEFAULT_STACK_SIZE);

  return result;
}


static void
set_cnf_root (Nenofex * nenofex)
{
  Node *and = and_node (nenofex);
  and->size_subformula = 1;     /* will be incremented when adding clauses */
  nenofex->graph_root = and;
}


static void
add_default_scope (Nenofex * nenofex)
{
  Scope *default_scope = new_scope (nenofex);
  default_scope->type = SCOPE_TYPE_EXISTENTIAL;
  default_scope->nesting = DEFAULT_SCOPE_NESTING;

  push_stack (nenofex->mm, nenofex->scopes, default_scope);

  assert (nenofex->scopes->elems[0] == default_scope);
}

static int is_unsigned_string (char *str);

static Var *
find_min_cost_var_in_scope (Nenofex * nenofex, Scope * scope)
{
  assert (!count_stack (nenofex->vars_marked_for_update));

  Var *min_cost_var = 0;
  Stack *scope_priority_heap = scope->priority_heap;

  while ((min_cost_var = remove_min (scope_priority_heap)))
    {
      if (variable_has_occs (min_cost_var))
        break;
      else
        {
          assert (0);
        }
    }

  nenofex->num_cur_remaining_scope_vars = count_stack (scope_priority_heap);

  return min_cost_var;
}


/*
- like 'find_min_cost_var_in_scope' but does not remove var from priority queue
*/
static Var *
peek_min_cost_var_in_scope (Nenofex * nenofex, Scope * scope)
{
  assert (!count_stack (nenofex->vars_marked_for_update));

  Var *min_cost_var = 0;
  Stack *scope_priority_heap = scope->priority_heap;

  while ((min_cost_var = access_min (scope_priority_heap)))
    {
      if (variable_has_occs (min_cost_var))
        break;
      else
        {
          assert (0);
        }
    }

  return min_cost_var;
}


#ifndef NDEBUG
/*
- for assertion checking only 
*/
static void
assert_all_subformula_sizes (Nenofex * nenofex)
{
  Stack *stack = create_stack (nenofex->mm, DEFAULT_STACK_SIZE);
  push_stack (nenofex->mm, stack, nenofex->graph_root);

  Node *cur;
  while ((cur = pop_stack (stack)))
    {
      if (is_literal_node (cur))
        {
          assert (cur->size_subformula == 1);
          cur->test_size_subformula = 1;
        }
      else
        {
          if (size_subformula_marked (cur))
            {
              size_subformula_unmark (cur);
              cur->test_size_subformula = 1;

              Node *child;
              for (child = cur->child_list.first; child;
                   child = child->level_link.next)
                cur->test_size_subformula += child->test_size_subformula;

              assert (cur->test_size_subformula == cur->size_subformula);
            }
          else                  /* recalculate sizes of children first */
            {
              size_subformula_mark (cur);
              push_stack (nenofex->mm, stack, cur);

              Node *child;
              for (child = cur->child_list.last; child;
                   child = child->level_link.prev)
                push_stack (nenofex->mm, stack, child);
            }
        }                       /* end: op-node */
    }                           /* end: while */

  delete_stack (nenofex->mm, stack);
}

#endif /* end ifndef NDEBUG */


/* 
- checks if there are any universally quantified variables left
- TODO: refinements
*/
static int
is_formula_existential (Nenofex * nenofex)
{
  int result = 1;

  void **v_scope, **scope_start;
  scope_start = nenofex->scopes->elems;
  for (v_scope = nenofex->scopes->top - 1;
       result && v_scope >= scope_start; v_scope--)
    {

      Scope *scope = *v_scope;
      if (is_universal_scope (scope))   /* check if all vars in scope eliminated */
        {
          void **v_var, **var_start;
          var_start = scope->vars->elems;
          for (v_var = scope->vars->top - 1; result && v_var >= var_start;
               v_var--)
            {
              Var *var = *v_var;
              result = (!variable_has_occs (var));
            }                   /* end: for all vars in scope */

          if (result)
            assert (is_empty_scope (nenofex, scope));
        }

    }                           /* end: for all scopes */

  return result;
}


/* 
- checks if there are any existentially quantified variables left
- TODO: refinements
*/
static int
is_formula_universal (Nenofex * nenofex)
{
  int result = 1;

  void **v_scope, **scope_start;
  scope_start = nenofex->scopes->elems;
  for (v_scope = nenofex->scopes->top - 1;
       result && v_scope >= scope_start; v_scope--)
    {

      Scope *scope = *v_scope;
      if (is_existential_scope (scope)) /* all vars in scope eliminated or have no occs left? */
        {
          void **v_var, **var_start;
          var_start = scope->vars->elems;
          for (v_var = scope->vars->top - 1; result && v_var >= var_start;
               v_var--)
            {
              Var *var = *v_var;
              result = (!variable_has_occs (var));
            }                   /* end: for all vars in scope */

          if (result)
            assert (is_empty_scope (nenofex, scope));
        }

    }                           /* end: for all scopes */

  return result;
}


/* 
- FOR DEBUGGING PURPOSES ONLY -> TODO: disable
- called before assigning IDs for tseitin transformation 
*/
static void
reset_all_node_ids (Nenofex * nenofex)
{
  Stack *stack = create_stack (nenofex->mm, DEFAULT_STACK_SIZE);
  push_stack (nenofex->mm, stack, nenofex->graph_root);

  Node *cur;
  while ((cur = pop_stack (stack)))
    {
      cur->id = 0;
      if (!is_literal_node (cur))
        {
          Node *ch;
          for (ch = cur->child_list.last; ch; ch = ch->level_link.prev)
            push_stack (nenofex->mm, stack, ch);
        }
    }

  delete_stack (nenofex->mm, stack);
}


/* NNF-TO-CNF CONVERSION */

/* ------- START: STANDARD TSEITIN TRANSFORMATION ------- */

static void
nnf_to_cnf_standard_tseitin_assign_node_ids (Nenofex * nenofex)
{
  reset_all_node_ids (nenofex);

  nenofex->tseitin_next_id = 1;

  void **v_scope, **scope_end;
  scope_end = nenofex->scopes->top;
  for (v_scope = nenofex->scopes->elems; v_scope < scope_end; v_scope++)
    {
      Scope *scope = *v_scope;
      void **v_var, **var_end;
      var_end = scope->vars->top;
      for (v_var = scope->vars->elems; v_var < var_end; v_var++)
        {
          Var *var = *v_var;
          if (variable_has_occs (var))
            {
              assert (!var->eliminated);
              var->id = nenofex->tseitin_next_id++;
            }
        }                       /* end: for all vars in scope */
    }                           /* end: for all scopes */

  nenofex->tseitin_first_op_node_id = nenofex->tseitin_next_id;

  /* traverse graph and assign IDs */

  Stack *stack = create_stack (nenofex->mm, DEFAULT_STACK_SIZE);
  push_stack (nenofex->mm, stack, nenofex->graph_root);

  Node *cur;
  while ((cur = pop_stack (stack)))
    {
      if (is_literal_node (cur))
        {
          Lit *lit = cur->lit;
          assert (lit->var->id > 0);
          assert (lit->var->id < nenofex->tseitin_first_op_node_id);
          cur->id = (lit->negated ? -lit->var->id : lit->var->id);
        }
      else
        {
          cur->id = nenofex->tseitin_next_id++;

          Node *child;
          for (child = cur->child_list.last; child;
               child = child->level_link.prev)
            push_stack (nenofex->mm, stack, child);
        }
    }                           /* end: while stack not empty */

  delete_stack (nenofex->mm, stack);
}


static int
nnf_to_cnf_standard_tseitin_count_clauses (Nenofex * nenofex, int qnnf)
{
  if (!nenofex->graph_root)
    return 0;

  if (is_literal_node (nenofex->graph_root))
    {
      return 1;
    }

  int clause_cnt = 1;           /* count output at root */

  if (qnnf)
    clause_cnt = 0;

  Stack *stack = create_stack (nenofex->mm, DEFAULT_STACK_SIZE);
  push_stack (nenofex->mm, stack, nenofex->graph_root);

  Node *cur;
  while ((cur = pop_stack (stack)))
    {
      if (!is_literal_node (cur))
        {
          clause_cnt += cur->num_children + 1;

          Node *child;
          for (child = cur->child_list.last; child;
               child = child->level_link.prev)
            push_stack (nenofex->mm, stack, child);
        }
    }                           /* end: while stack not empty */

  delete_stack (nenofex->mm, stack);

  return clause_cnt;
}


/* 
- assumes that IDs have been assigned to nodes
- dumps CNF to 'out'
*/
static void
nnf_to_cnf_standard_tseitin_dump (Nenofex * nenofex, FILE * out, int qnnf)
{
  assert (nenofex->graph_root);
  assert (qnnf || !is_formula_existential (nenofex)
          || !nenofex->sat_solver_tautology_mode);
  assert (qnnf || nenofex->sat_solver_tautology_mode
          || is_formula_existential (nenofex));

  assert (qnnf || !is_formula_universal (nenofex)
          || nenofex->sat_solver_tautology_mode);
  assert (qnnf || !nenofex->sat_solver_tautology_mode
          || is_formula_universal (nenofex));

  int num_clauses = nnf_to_cnf_standard_tseitin_count_clauses (nenofex, qnnf);
  fprintf (out, "p cnf %d %d\n", nenofex->tseitin_next_id - 1, num_clauses);

  if (qnnf)
    {
      /* Print prefix where tseitin variables occur in innermost
         (existential) scope. */
      void **v_scope, **scope_end;
      scope_end = nenofex->scopes->top;
      for (v_scope = nenofex->scopes->elems; v_scope < scope_end; v_scope++)
        {
          Scope *scope = *v_scope;
          fprintf (out, "%c ", is_existential_scope (scope) ? 'e' : 'a');
          void **v_var, **var_end;
          var_end = scope->vars->top;
          for (v_var = scope->vars->elems; v_var < var_end; v_var++)
            {
              Var *var = *v_var;
              if (variable_has_occs (var))
                {
                  assert (!var->eliminated);
                  assert (var->id);
                  fprintf (out, "%d ", var->id);
                }
            }                   /* end: for all vars in scope */

          /* Must print tseitin variables in innermost scope. */
          if (v_scope == scope_end - 1)
            {
              fprintf (stderr, "Dump CNF: first,last tseitin id: %d,%d\n",
                       nenofex->tseitin_first_op_node_id,
                       nenofex->tseitin_next_id - 1);

              if (!is_existential_scope (scope))
                {
                  /* Could have innermost universal scope after
                     expansions. First close that scope and open new
                     existential one. */
                  fprintf (out, "0\n");
                  fprintf (out, "e ");
                }
              unsigned int tvar, tvar_end;
              for (tvar = nenofex->tseitin_first_op_node_id,
                   tvar_end = nenofex->tseitin_next_id; tvar < tvar_end;
                   tvar++)
                fprintf (out, "%d ", tvar);
            }

          fprintf (out, "0\n");
        }                       /* end: for all scopes */
    }

  assert (nenofex->graph_root->id);

  if (!qnnf)
    {
      int output = nenofex->sat_solver_tautology_mode ?
        -nenofex->graph_root->id : nenofex->graph_root->id;
      fprintf (out, "%d 0\n", output);
    }

  Stack *stack = create_stack (nenofex->mm, DEFAULT_STACK_SIZE);
  push_stack (nenofex->mm, stack, nenofex->graph_root);

  Node *cur;
  while ((cur = pop_stack (stack)))
    {
      if (is_and_node (cur))
        {
          assert (cur->id > 0);

          Node *child;
          for (child = cur->child_list.first; child;
               child = child->level_link.next)
            {
              assert (child->id);
              fprintf (out, "%d %d 0\n", -cur->id, child->id);
            }

          for (child = cur->child_list.first; child;
               child = child->level_link.next)
            {
              assert (child->id);
              fprintf (out, "%d ", -child->id);
            }
          fprintf (out, "%d 0\n", cur->id);

          /* TODO: pushing children could be done in loop before */
          for (child = cur->child_list.last; child;
               child = child->level_link.prev)
            push_stack (nenofex->mm, stack, child);
        }
      else if (is_or_node (cur))
        {
          assert (cur->id > 0);

          Node *child;
          fprintf (out, "%d ", -cur->id);
          for (child = cur->child_list.first; child;
               child = child->level_link.next)
            {
              assert (child->id);
              fprintf (out, "%d ", child->id);
            }
          fprintf (out, "0\n");

          for (child = cur->child_list.first; child;
               child = child->level_link.next)
            {
              assert (child->id);
              fprintf (out, "%d %d 0\n", cur->id, -child->id);
            }

          /* TODO: pushing children could be done in loop before */
          for (child = cur->child_list.last; child;
               child = child->level_link.prev)
            push_stack (nenofex->mm, stack, child);
        }
    }                           /* end: while stack not empty */

  delete_stack (nenofex->mm, stack);
}


/* 
- assumes that IDs have been assigned to nodes
- same code like in dumping but CNF is forwarded to internal SAT solver
*/
static void
nnf_to_cnf_standard_tseitin_forward (Nenofex * nenofex)
{
  assert (nenofex->graph_root);

  assert (!is_formula_existential (nenofex)
          || !nenofex->sat_solver_tautology_mode);
  assert (nenofex->sat_solver_tautology_mode
          || is_formula_existential (nenofex));

  assert (!is_formula_universal (nenofex)
          || nenofex->sat_solver_tautology_mode);
  assert (!nenofex->sat_solver_tautology_mode
          || is_formula_universal (nenofex));

  assert (nenofex->graph_root->id);

  int output = nenofex->sat_solver_tautology_mode ?
    -nenofex->graph_root->id : nenofex->graph_root->id;
  sat_solver_add (nenofex, output);
  sat_solver_add (nenofex, 0);

  Stack *stack = create_stack (nenofex->mm, DEFAULT_STACK_SIZE);
  push_stack (nenofex->mm, stack, nenofex->graph_root);

  Node *cur;
  while ((cur = pop_stack (stack)))
    {
      if (is_and_node (cur))
        {
          assert (cur->id > 0);

          Node *child;
          for (child = cur->child_list.first; child;
               child = child->level_link.next)
            {
              assert (child->id);
              sat_solver_add (nenofex, -cur->id);
              sat_solver_add (nenofex, child->id);
              sat_solver_add (nenofex, 0);
            }

          for (child = cur->child_list.first; child;
               child = child->level_link.next)
            {
              assert (child->id);
              sat_solver_add (nenofex, -child->id);
            }
          sat_solver_add (nenofex, cur->id);
          sat_solver_add (nenofex, 0);

          /* TODO: pushing children could be done in loop before */
          for (child = cur->child_list.last; child;
               child = child->level_link.prev)
            push_stack (nenofex->mm, stack, child);
        }
      else if (is_or_node (cur))
        {
          assert (cur->id > 0);

          Node *child;
          sat_solver_add (nenofex, -cur->id);
          for (child = cur->child_list.first; child;
               child = child->level_link.next)
            {
              assert (child->id);
              sat_solver_add (nenofex, child->id);
            }
          sat_solver_add (nenofex, 0);

          for (child = cur->child_list.first; child;
               child = child->level_link.next)
            {
              assert (child->id);

              sat_solver_add (nenofex, cur->id);
              sat_solver_add (nenofex, -child->id);
              sat_solver_add (nenofex, 0);
            }

          /* TODO: pushing children could be done in loop before */
          for (child = cur->child_list.last; child;
               child = child->level_link.prev)
            push_stack (nenofex->mm, stack, child);
        }
    }                           /* end: while stack not empty */

  delete_stack (nenofex->mm, stack);
}

/* ------- END: STANDARD TSEITIN TRANSFORMATION ------- */


/* ------- START: REVISED TSEITIN TRANSFORMATION ------- */

static void
nnf_to_cnf_tseitin_revised_assign_node_ids (Nenofex * nenofex)
{
  reset_all_node_ids (nenofex);

  nenofex->tseitin_next_id = 1;

  void **v_scope, **scope_end;
  scope_end = nenofex->scopes->top;
  for (v_scope = nenofex->scopes->elems; v_scope < scope_end; v_scope++)
    {
      Scope *scope = *v_scope;
      void **v_var, **var_end;
      var_end = scope->vars->top;
      for (v_var = scope->vars->elems; v_var < var_end; v_var++)
        {
          Var *var = *v_var;
          if (variable_has_occs (var))
            {
              assert (!var->eliminated);
              var->id = nenofex->tseitin_next_id++;
            }
        }                       /* end: for all vars in scope */
    }                           /* end: for all scopes */

  nenofex->tseitin_first_op_node_id = nenofex->tseitin_next_id;

  /* traverse graph and assign IDs */

  if (is_literal_node (nenofex->graph_root))
    {
      Lit *lit = nenofex->graph_root->lit;
      nenofex->graph_root->id = (lit->negated ? -lit->var->id : lit->var->id);
      return;
    }

  Stack *stack = create_stack (nenofex->mm, DEFAULT_STACK_SIZE);

  if (is_and_node (nenofex->graph_root))
    {
      if (nenofex->sat_solver_tautology_mode)
        {
          Node *child;
          for (child = nenofex->graph_root->child_list.last;
               child; child = child->level_link.prev)
            {
              assert (!is_and_node (child));
              if (!is_literal_node (child))
                push_stack (nenofex->mm, stack, child);
              else
                {
                  Lit *lit = child->lit;
                  assert (lit->var->id > 0);
                  assert (lit->var->id < nenofex->tseitin_first_op_node_id);
                  child->id = (lit->negated ? -lit->var->id : lit->var->id);
                }
            }
        }
      else                      /* sat-mode */
        {
          Node *child;
          for (child = nenofex->graph_root->child_list.last;
               child; child = child->level_link.prev)
            {
              if (!is_literal_node (child))
                {
                  Node *child_child;
                  for (child_child = child->child_list.last;
                       child_child;
                       child_child = child_child->level_link.prev)
                    {
                      if (!is_literal_node (child_child))
                        {
                          push_stack (nenofex->mm, stack, child_child);
                        }
                      else
                        {
                          Lit *lit = child_child->lit;
                          assert (lit->var->id > 0);
                          assert (lit->var->id <
                                  nenofex->tseitin_first_op_node_id);
                          child_child->id =
                            (lit->negated ? -lit->var->id : lit->var->id);
                        }
                    }           /* end: for child's children */
                }
              else
                {
                  Lit *lit = child->lit;
                  assert (lit->var->id > 0);
                  assert (lit->var->id < nenofex->tseitin_first_op_node_id);
                  child->id = (lit->negated ? -lit->var->id : lit->var->id);
                }
            }                   /* end: for all children */
        }                       /* end: sat mode */
    }
  else                          /* OR */
    {
      if (!nenofex->sat_solver_tautology_mode)
        {
          Node *child;
          for (child = nenofex->graph_root->child_list.last;
               child; child = child->level_link.prev)
            {
              assert (!is_or_node (child));
              if (!is_literal_node (child))
                push_stack (nenofex->mm, stack, child);
              else
                {
                  Lit *lit = child->lit;
                  assert (lit->var->id > 0);
                  assert (lit->var->id < nenofex->tseitin_first_op_node_id);
                  child->id = (lit->negated ? -lit->var->id : lit->var->id);
                }
            }
        }
      else                      /* sat mode */
        {
          Node *child;
          for (child = nenofex->graph_root->child_list.last;
               child; child = child->level_link.prev)
            {
              if (!is_literal_node (child))
                {
                  Node *child_child;
                  for (child_child = child->child_list.last;
                       child_child;
                       child_child = child_child->level_link.prev)
                    {
                      if (!is_literal_node (child_child))
                        {
                          push_stack (nenofex->mm, stack, child_child);
                        }
                      else
                        {
                          Lit *lit = child_child->lit;
                          assert (lit->var->id > 0);
                          assert (lit->var->id <
                                  nenofex->tseitin_first_op_node_id);
                          child_child->id =
                            (lit->negated ? -lit->var->id : lit->var->id);
                        }
                    }           /* end: for child's children */
                }
              else
                {
                  Lit *lit = child->lit;
                  assert (lit->var->id > 0);
                  assert (lit->var->id < nenofex->tseitin_first_op_node_id);
                  child->id = (lit->negated ? -lit->var->id : lit->var->id);
                }
            }                   /* end: for all children */
        }                       /* end: sat mode */
    }                           /* end: OR */

  Node *cur;
  while ((cur = pop_stack (stack)))
    {
      assert (nenofex->sat_solver_tautology_mode || is_and_node (cur));
      assert (!is_and_node (cur) || !nenofex->sat_solver_tautology_mode);

      assert (!nenofex->sat_solver_tautology_mode || is_or_node (cur));
      assert (!is_or_node (cur) || nenofex->sat_solver_tautology_mode);

      cur->id = nenofex->tseitin_next_id++;

      Node *child;
      for (child = cur->child_list.last; child;
           child = child->level_link.prev)
        {
          if (!is_literal_node (child))
            {
              Node *child_child;
              for (child_child = child->child_list.last;
                   child_child; child_child = child_child->level_link.prev)
                {
                  if (!is_literal_node (child_child))
                    {
                      push_stack (nenofex->mm, stack, child_child);
                    }
                  else
                    {
                      Lit *lit = child_child->lit;
                      assert (lit->var->id > 0);
                      assert (lit->var->id <
                              nenofex->tseitin_first_op_node_id);
                      child_child->id =
                        (lit->negated ? -lit->var->id : lit->var->id);
                    }
                }               /* end: for child's children */
            }
          else
            {
              Lit *lit = child->lit;
              assert (lit->var->id > 0);
              assert (lit->var->id < nenofex->tseitin_first_op_node_id);
              child->id = (lit->negated ? -lit->var->id : lit->var->id);
            }
        }                       /* end: for all children */

    }                           /* end: while stack not empty */

  delete_stack (nenofex->mm, stack);
}


static int
nnf_to_cnf_tseitin_revised_count_clauses (Nenofex * nenofex)
{
  if (!nenofex->graph_root)
    return 0;

#ifndef NDEBUG
  if (nenofex->cur_expansions != 0)
    {
      assert (!is_formula_existential (nenofex)
              || !nenofex->sat_solver_tautology_mode);
      assert (nenofex->sat_solver_tautology_mode
              || is_formula_existential (nenofex));

      assert (!is_formula_universal (nenofex)
              || nenofex->sat_solver_tautology_mode);
      assert (!nenofex->sat_solver_tautology_mode
              || is_formula_universal (nenofex));
    }
#endif

  if (is_literal_node (nenofex->graph_root))
    {
      return 1;
    }

  int clause_cnt = 0;

  Stack *stack = create_stack (nenofex->mm, DEFAULT_STACK_SIZE);

  if (is_and_node (nenofex->graph_root))
    {
      if (nenofex->sat_solver_tautology_mode)
        {
          clause_cnt++;         /* one clause for top AND */
          Node *child;
          for (child = nenofex->graph_root->child_list.last;
               child; child = child->level_link.prev)
            {
              assert (!is_and_node (child));
              if (!is_literal_node (child))
                push_stack (nenofex->mm, stack, child);
            }
        }
      else
        push_stack (nenofex->mm, stack, nenofex->graph_root);
    }
  else                          /* OR */
    {
      if (!nenofex->sat_solver_tautology_mode)
        {
          clause_cnt++;         /* one clause for top-OR */
          Node *child;
          for (child = nenofex->graph_root->child_list.last;
               child; child = child->level_link.prev)
            {
              assert (!is_or_node (child));
              if (!is_literal_node (child))
                push_stack (nenofex->mm, stack, child);
            }
        }
      else
        push_stack (nenofex->mm, stack, nenofex->graph_root);
    }

  Node *cur;
  while ((cur = pop_stack (stack)))
    {
      assert (nenofex->sat_solver_tautology_mode || is_and_node (cur));
      assert (!is_and_node (cur) || !nenofex->sat_solver_tautology_mode);

      assert (!nenofex->sat_solver_tautology_mode || is_or_node (cur));
      assert (!is_or_node (cur) || nenofex->sat_solver_tautology_mode);

      clause_cnt += cur->num_children;

      Node *child;
      for (child = cur->child_list.last; child;
           child = child->level_link.prev)
        {
          if (!is_literal_node (child))
            {
              Node *child_child;
              for (child_child = child->child_list.last;
                   child_child; child_child = child_child->level_link.prev)
                {
                  if (!is_literal_node (child_child))
                    {
                      push_stack (nenofex->mm, stack, child_child);
                    }
                }               /* end: for child's children */
            }
        }                       /* end: for all children */

    }                           /* end: while stack not empty */

  delete_stack (nenofex->mm, stack);

  return clause_cnt;
}


/*
- sat mode
*/
static void
nnf_to_cnf_tseitin_revised_top_truth_dump (Nenofex * nenofex, FILE * out)
{
  assert (nenofex->graph_root);
  assert (is_formula_existential (nenofex));
  assert (!nenofex->sat_solver_tautology_mode);

  int num_clauses = nnf_to_cnf_tseitin_revised_count_clauses (nenofex);
  fprintf (out, "p cnf %d %d\n", nenofex->tseitin_next_id - 1, num_clauses);

  if (is_literal_node (nenofex->graph_root))
    {
      assert (nenofex->graph_root->id);
      fprintf (out, "%d 0\n", nenofex->graph_root->id);
      return;
    }

  Stack *stack = create_stack (nenofex->mm, DEFAULT_STACK_SIZE);

  if (is_and_node (nenofex->graph_root))
    {
      Node *child;
      for (child = nenofex->graph_root->child_list.last;
           child; child = child->level_link.prev)
        {                       /* each 'child' generates a clause where child's children make up set of literals */
          if (is_literal_node (child))
            {
              assert (child->id);
              fprintf (out, "%d 0\n", child->id);
            }
          else                  /* OR */
            {
              Node *child_child;
              for (child_child = child->child_list.last;
                   child_child; child_child = child_child->level_link.prev)
                {
                  assert (child_child->id);
                  fprintf (out, "%d ", child_child->id);
                  if (!is_literal_node (child_child))
                    push_stack (nenofex->mm, stack, child_child);
                }               /* end: for all child's children */
              fprintf (out, "0\n");
            }
        }                       /* end: for AND's children */
    }
  else                          /* root is OR */
    {
      Node *child;
      for (child = nenofex->graph_root->child_list.last;
           child; child = child->level_link.prev)
        {
          assert (child->id);
          fprintf (out, "%d ", child->id);      /* print top-or constraint */
          assert (!is_or_node (child));
          if (!is_literal_node (child))
            push_stack (nenofex->mm, stack, child);
        }
      fprintf (out, "0\n");
    }

  Node *cur;
  while ((cur = pop_stack (stack)))
    {
      assert (is_and_node (cur));
      assert (cur->id);

      Node *child;
      for (child = cur->child_list.last; child;
           child = child->level_link.prev)
        {                       /* each 'child' generates a clause where child's children make up set of literals */
          fprintf (out, "%d ", -cur->id);
          if (is_literal_node (child))
            {
              assert (child->id);
              fprintf (out, "%d 0\n", child->id);
            }
          else                  /* OR */
            {
              Node *child_child;
              for (child_child = child->child_list.last;
                   child_child; child_child = child_child->level_link.prev)
                {
                  assert (child_child->id);
                  fprintf (out, "%d ", child_child->id);
                  if (!is_literal_node (child_child))
                    push_stack (nenofex->mm, stack, child_child);
                }               /* end: for all child's children */
              fprintf (out, "0\n");
            }
        }                       /* end: for AND's children */

    }                           /* end: while stack not empty */

  delete_stack (nenofex->mm, stack);
}


/*
- same code as in dumping but now forward to internal sat solver
*/
static void
nnf_to_cnf_tseitin_revised_top_truth_forward (Nenofex * nenofex)
{
  assert (nenofex->graph_root);
  assert (is_formula_existential (nenofex));
  assert (!nenofex->sat_solver_tautology_mode);

  if (is_literal_node (nenofex->graph_root))
    {
      assert (nenofex->graph_root->id);
      sat_solver_add (nenofex, nenofex->graph_root->id);
      sat_solver_add (nenofex, 0);
      return;
    }

  Stack *stack = create_stack (nenofex->mm, DEFAULT_STACK_SIZE);

  if (is_and_node (nenofex->graph_root))
    {
      Node *child;
      for (child = nenofex->graph_root->child_list.last;
           child; child = child->level_link.prev)
        {                       /* each 'child' generates a clause where child's children make up set of literals */
          if (is_literal_node (child))
            {
              assert (child->id);
              sat_solver_add (nenofex, child->id);
              sat_solver_add (nenofex, 0);
            }
          else                  /* OR */
            {
              Node *child_child;
              for (child_child = child->child_list.last;
                   child_child; child_child = child_child->level_link.prev)
                {
                  assert (child_child->id);
                  sat_solver_add (nenofex, child_child->id);
                  if (!is_literal_node (child_child))
                    push_stack (nenofex->mm, stack, child_child);
                }               /* end: for all child's children */
              sat_solver_add (nenofex, 0);
            }
        }                       /* end: for AND's children */
    }
  else                          /* root is OR */
    {
      Node *child;
      for (child = nenofex->graph_root->child_list.last;
           child; child = child->level_link.prev)
        {
          assert (child->id);
          sat_solver_add (nenofex, child->id);
          assert (!is_or_node (child));
          if (!is_literal_node (child))
            push_stack (nenofex->mm, stack, child);
        }
      sat_solver_add (nenofex, 0);
    }

  Node *cur;
  while ((cur = pop_stack (stack)))
    {
      assert (is_and_node (cur));
      assert (cur->id);

      Node *child;
      for (child = cur->child_list.last; child;
           child = child->level_link.prev)
        {                       /* each 'child' generates a clause where child's children make up set of literals */
          sat_solver_add (nenofex, -cur->id);
          if (is_literal_node (child))
            {
              assert (child->id);
              sat_solver_add (nenofex, child->id);
              sat_solver_add (nenofex, 0);
            }
          else                  /* OR */
            {
              Node *child_child;
              for (child_child = child->child_list.last;
                   child_child; child_child = child_child->level_link.prev)
                {
                  assert (child_child->id);
                  sat_solver_add (nenofex, child_child->id);
                  if (!is_literal_node (child_child))
                    push_stack (nenofex->mm, stack, child_child);
                }               /* end: for all child's children */
              sat_solver_add (nenofex, 0);
            }
        }                       /* end: for AND's children */

    }                           /* end: while stack not empty */

  delete_stack (nenofex->mm, stack);
}


/*
- tautology mode
*/
static void
nnf_to_cnf_tseitin_revised_top_falsity_dump (Nenofex * nenofex, FILE * out)
{
  assert (nenofex->graph_root);
  assert (is_formula_universal (nenofex));
  assert (nenofex->sat_solver_tautology_mode);

  int num_clauses = nnf_to_cnf_tseitin_revised_count_clauses (nenofex);
  fprintf (out, "p cnf %d %d\n", nenofex->tseitin_next_id - 1, num_clauses);

  if (is_literal_node (nenofex->graph_root))
    {
      assert (nenofex->graph_root->id);
      fprintf (out, "%d 0\n", -nenofex->graph_root->id);
      return;
    }

  Stack *stack = create_stack (nenofex->mm, DEFAULT_STACK_SIZE);

  if (is_or_node (nenofex->graph_root))
    {
      Node *child;
      for (child = nenofex->graph_root->child_list.last;
           child; child = child->level_link.prev)
        {                       /* each 'child' generates a clause where child's children make up set of literals */
          if (is_literal_node (child))
            {
              assert (child->id);
              fprintf (out, "%d 0\n", -child->id);
            }
          else                  /* AND */
            {
              Node *child_child;
              for (child_child = child->child_list.last;
                   child_child; child_child = child_child->level_link.prev)
                {
                  assert (child_child->id);
                  fprintf (out, "%d ", -child_child->id);
                  if (!is_literal_node (child_child))
                    push_stack (nenofex->mm, stack, child_child);
                }               /* end: for all child's children */
              fprintf (out, "0\n");
            }
        }                       /* end: for OR's children */
    }
  else                          /* root is AND */
    {
      Node *child;
      for (child = nenofex->graph_root->child_list.last;
           child; child = child->level_link.prev)
        {
          assert (child->id);
          fprintf (out, "%d ", -child->id);     /* print top-and constraint */
          assert (!is_and_node (child));
          if (!is_literal_node (child))
            push_stack (nenofex->mm, stack, child);
        }
      fprintf (out, "0\n");
    }

  Node *cur;
  while ((cur = pop_stack (stack)))
    {
      assert (is_or_node (cur));
      assert (cur->id);

      Node *child;
      for (child = cur->child_list.last; child;
           child = child->level_link.prev)
        {                       /* each 'child' generates a clause where child's children make up set of literals */
          fprintf (out, "%d ", cur->id);
          if (is_literal_node (child))
            {
              assert (child->id);
              fprintf (out, "%d 0\n", -child->id);
            }
          else                  /* AND */
            {
              Node *child_child;
              for (child_child = child->child_list.last;
                   child_child; child_child = child_child->level_link.prev)
                {
                  assert (child_child->id);
                  fprintf (out, "%d ", -child_child->id);
                  if (!is_literal_node (child_child))
                    push_stack (nenofex->mm, stack, child_child);
                }               /* end: for all child's children */
              fprintf (out, "0\n");
            }
        }                       /* end: for OR's children */

    }                           /* end: while stack not empty */

  delete_stack (nenofex->mm, stack);
}


/*
- same code as in dumping but now forward to internal sat solver
*/
static void
nnf_to_cnf_tseitin_revised_top_falsity_forward (Nenofex * nenofex)
{
  assert (nenofex->graph_root);
  assert (is_formula_universal (nenofex));
  assert (nenofex->sat_solver_tautology_mode);

  if (is_literal_node (nenofex->graph_root))
    {
      assert (nenofex->graph_root->id);
      sat_solver_add (nenofex, -nenofex->graph_root->id);
      sat_solver_add (nenofex, 0);
      return;
    }

  Stack *stack = create_stack (nenofex->mm, DEFAULT_STACK_SIZE);

  if (is_or_node (nenofex->graph_root))
    {
      Node *child;
      for (child = nenofex->graph_root->child_list.last; child;
           child = child->level_link.prev)
        {                       /* each 'child' generates a clause where child's children make up set of literals */
          if (is_literal_node (child))
            {
              assert (child->id);
              sat_solver_add (nenofex, -child->id);
              sat_solver_add (nenofex, 0);
            }
          else                  /* AND */
            {
              Node *child_child;
              for (child_child = child->child_list.last;
                   child_child; child_child = child_child->level_link.prev)
                {
                  assert (child_child->id);
                  sat_solver_add (nenofex, -child_child->id);
                  if (!is_literal_node (child_child))
                    push_stack (nenofex->mm, stack, child_child);
                }               /* end: for all child's children */
              sat_solver_add (nenofex, 0);
            }
        }                       /* end: for AND's children */
    }
  else                          /* root is AND */
    {
      Node *child;
      for (child = nenofex->graph_root->child_list.last;
           child; child = child->level_link.prev)
        {
          assert (child->id);
          sat_solver_add (nenofex, -child->id);
          assert (!is_and_node (child));
          if (!is_literal_node (child))
            push_stack (nenofex->mm, stack, child);
        }
      sat_solver_add (nenofex, 0);
    }

  Node *cur;
  while ((cur = pop_stack (stack)))
    {
      assert (is_or_node (cur));
      assert (cur->id);

      Node *child;
      for (child = cur->child_list.last; child;
           child = child->level_link.prev)
        {                       /* each 'child' generates a clause where child's children make up set of literals */
          sat_solver_add (nenofex, cur->id);
          if (is_literal_node (child))
            {
              assert (child->id);
              sat_solver_add (nenofex, -child->id);
              sat_solver_add (nenofex, 0);
            }
          else                  /* AND */
            {
              Node *child_child;
              for (child_child = child->child_list.last;
                   child_child; child_child = child_child->level_link.prev)
                {
                  assert (child_child->id);
                  sat_solver_add (nenofex, -child_child->id);
                  if (!is_literal_node (child_child))
                    push_stack (nenofex->mm, stack, child_child);
                }               /* end: for all child's children */
              sat_solver_add (nenofex, 0);
            }
        }                       /* end: for AND's children */

    }                           /* end: while stack not empty */

  delete_stack (nenofex->mm, stack);
}

/* ------- END: REVISED TSEITIN TRANSFORMATION ------- */


static int count_variables (Nenofex * nenofex, const int count_existential);


static void
quantified_nnf_to_cnf_dump (Nenofex * nenofex, FILE * out)
{
  int num_clauses = 0, num_vars = 0, num_remaining_vars = 0,
    num_remaining_exist_vars = 0, num_remaining_univ_vars = 0;

  /* Use standard-tseitin encoding. */
  nnf_to_cnf_standard_tseitin_assign_node_ids (nenofex);
  num_clauses = nnf_to_cnf_standard_tseitin_count_clauses (nenofex, 1);
  num_vars = nenofex->tseitin_next_id - 1;

  fprintf (stderr, "\nDumped CNF:\n");
  fprintf (stderr, "  tseitin variables: %d\n", num_vars);
  fprintf (stderr, "  tseitin clauses: %d\n", num_clauses);
  nnf_to_cnf_standard_tseitin_dump (nenofex, out, 1);
}


static void
nnf_to_cnf_dump (Nenofex * nenofex, FILE * out)
{
  int num_clauses = 0, num_vars = 0, num_remaining_vars = 0,
    num_remaining_exist_vars = 0, num_remaining_univ_vars = 0;

  if (nenofex->options.cnf_generator_tseitin_revised_specified)
    {
      nnf_to_cnf_tseitin_revised_assign_node_ids (nenofex);
      num_clauses = nnf_to_cnf_tseitin_revised_count_clauses (nenofex);
    }
  else
    {
      nnf_to_cnf_standard_tseitin_assign_node_ids (nenofex);
      num_clauses = nnf_to_cnf_standard_tseitin_count_clauses (nenofex, 0);
    }

  num_vars = nenofex->tseitin_next_id - 1;
  num_remaining_exist_vars = count_variables (nenofex, 1);
  num_remaining_univ_vars = count_variables (nenofex, 0);
  num_remaining_vars = num_remaining_exist_vars + num_remaining_univ_vars;

  fprintf (stderr, "\nDumped CNF:\n");
  fprintf (stderr, "  tseitin variables: %d\n", num_vars);
  fprintf (stderr, "  tseitin clauses: %d\n", num_clauses);

  if (nenofex->sat_solver_tautology_mode)
    {
      if (nenofex->options.cnf_generator_tseitin_revised_specified)
        nnf_to_cnf_tseitin_revised_top_falsity_dump (nenofex, out);
      else
        nnf_to_cnf_standard_tseitin_dump (nenofex, out, 0);
    }
  else
    {
      if (nenofex->options.cnf_generator_tseitin_revised_specified)
        nnf_to_cnf_tseitin_revised_top_truth_dump (nenofex, out);
      else
        nnf_to_cnf_standard_tseitin_dump (nenofex, out, 0);
    }
}


static void
nnf_to_cnf_forward (Nenofex * nenofex)
{
  int num_clauses = 0, num_vars = 0, num_remaining_vars = 0,
    num_remaining_exist_vars = 0, num_remaining_univ_vars = 0;

  if (nenofex->options.cnf_generator_tseitin_revised_specified)
    {
      nnf_to_cnf_tseitin_revised_assign_node_ids (nenofex);
      num_clauses = nnf_to_cnf_tseitin_revised_count_clauses (nenofex);
    }
  else
    {
      nnf_to_cnf_standard_tseitin_assign_node_ids (nenofex);
      num_clauses = nnf_to_cnf_standard_tseitin_count_clauses (nenofex, 0);
    }

  num_vars = nenofex->tseitin_next_id - 1;
  num_remaining_exist_vars = count_variables (nenofex, 1);
  num_remaining_univ_vars = count_variables (nenofex, 0);
  num_remaining_vars = num_remaining_exist_vars + num_remaining_univ_vars;

  if (!nenofex->options.print_short_answer_specified)
    {
      fprintf (stderr, "\nForwarded CNF:\n");
      fprintf (stderr, "  tseitin variables: %d\n", num_vars);
      fprintf (stderr, "  tseitin clauses: %d\n", num_clauses);
    }

  if (nenofex->sat_solver_tautology_mode)
    {
      if (nenofex->options.cnf_generator_tseitin_revised_specified)
        nnf_to_cnf_tseitin_revised_top_falsity_forward (nenofex);
      else
        nnf_to_cnf_standard_tseitin_forward (nenofex);
    }
  else
    {
      if (nenofex->options.cnf_generator_tseitin_revised_specified)
        nnf_to_cnf_tseitin_revised_top_truth_forward (nenofex);
      else
        nnf_to_cnf_standard_tseitin_forward (nenofex);
    }
}


/*
- does NOT yet work properly 
- TODO: REVISION - currently variables' IDs are all reassigned from scratch
*/
static void
get_var_assignments_from_sat_solver (Nenofex * nenofex)
{

#ifndef NDEBUG
  do
    {
      void **v_isp = nenofex->scopes->elems;
      Scope *scope = *v_isp;
      assert (scope->nesting == DEFAULT_SCOPE_NESTING);
      if (count_stack (scope->vars) == 0)       /* QBF instance */
        {
          v_isp++;
          scope = *v_isp;
          assert (scope->nesting == 1);
        }

      if (is_universal_scope (scope))
        assert (nenofex->result == NENOFEX_RESULT_UNSAT);
      else
        assert (nenofex->result == NENOFEX_RESULT_SAT);
    }
  while (0);
#endif

  void **v_scope, **scope_end;
  scope_end = nenofex->scopes->top;
  for (v_scope = nenofex->scopes->elems; v_scope < scope_end; v_scope++)
    {
      Scope *scope = *v_scope;
      void **v_var, **var_end;
      var_end = scope->vars->top;
      for (v_var = scope->vars->elems; v_var < var_end; v_var++)
        {
          Var *var = *v_var;
          if (variable_has_occs (var))
            {
              assert (!var->eliminated);
              assert (var->id > 0);

              int sat_solver_deref = sat_solver_deref (nenofex, var->id);
              VarAssignment assignment;
              if (sat_solver_deref > 0)
                assignment = VAR_ASSIGNMENT_TRUE;
              else if (sat_solver_deref < 0)
                assignment = VAR_ASSIGNMENT_FALSE;
              else
                assignment = VAR_ASSIGNMENT_UNDEFINED;
              var->assignment = assignment;
            }
        }                       /* end: for all vars in scope */
    }                           /* end: for all scopes */
}


/*
- does NOT yet work properly 
- TODO: REVISION - currently variables' IDs are all reassigned from scratch
*/
static void
generate_qdimacs_output (Nenofex * nenofex, FILE * out)
{
  assert (nenofex->result != NENOFEX_RESULT_UNKNOWN);

  int answer;
  if (nenofex->result == NENOFEX_RESULT_SAT)
    answer = 1;
  else if (nenofex->result == NENOFEX_RESULT_UNSAT)
    answer = 0;
  else
    answer = -1;

  fprintf (out, "s cnf %d %d %d\n", answer, nenofex->num_orig_vars,
           nenofex->num_orig_clauses);

  void **v_isp = nenofex->scopes->elems;
  Scope *scope = *v_isp;
  assert (scope->nesting == DEFAULT_SCOPE_NESTING);
  if (count_stack (scope->vars) == 0)   /* QBF instance */
    {
      v_isp++;
      scope = *v_isp;
      assert (scope->nesting == 1);
    }

  void **v_var, **var_end;
  var_end = scope->vars->top;
  for (v_var = scope->vars->elems; v_var < var_end; v_var++)
    {
      Var *var = *v_var;
      assert (var->id > 0);
      int value = var->assignment - 1;
      assert (var->assignment != VAR_ASSIGNMENT_UNDEFINED || value == -1);
      assert (var->assignment != VAR_ASSIGNMENT_FALSE || value == 0);
      assert (var->assignment != VAR_ASSIGNMENT_TRUE || value == 1);

      /* likely to fail.. */
      assert (var->assignment != VAR_ASSIGNMENT_UNDEFINED);

      int lit = var->id;
      if (var->assignment == VAR_ASSIGNMENT_FALSE)
        lit = -lit;
      fprintf (out, "V %d \n", lit);
    }
}


static int
is_unsigned_string (char *str)
{
  int result;
  char *p = str;

  result = p && *p;
  while (p && *p && (result = isdigit (*p++)))
    ;

  return result;
}


static void
set_default_cmd_line_options (Nenofex * nenofex)
{
  nenofex->options.cnf_generator_tseitin_revised_specified = 1;
  nenofex->options.cnf_generator_tseitin_specified = 0;

  nenofex->options.opt_subgraph_limit_specified = 1;
  nenofex->options.opt_subgraph_limit = 500;

  nenofex->options.univ_trigger = 10;
  nenofex->options.univ_trigger_delta = 10;

  nenofex->options.print_short_answer_specified = 1;
}


#ifndef NDEBUG
/*
- for assertion checking only
*/
static void
assert_solver_options (Nenofex * nenofex)
{
  assert (!nenofex->options.num_expansions_specified ||
          nenofex->options.num_expansions > 0);
  assert (nenofex->options.num_expansions <= 0 ||
          nenofex->options.num_expansions_specified);

  assert (!nenofex->options.cnf_generator_tseitin_specified ||
          !nenofex->options.cnf_generator_tseitin_revised_specified);
  assert (nenofex->options.cnf_generator_tseitin_revised_specified ||
          nenofex->options.cnf_generator_tseitin_specified);

  assert (!nenofex->options.size_cutoff_absolute_specified ||
          !nenofex->options.size_cutoff_relative_specified);
}
#endif




/*
- traverse LCA of unit variable and mark all occurring variables 
*/
static void
simplify_mark_lca_variables_for_update (Nenofex * nenofex, Var * var,
                                        Stack * node_stack)
{
  assert (!count_stack (node_stack));

  Node **ch, *child;
  for (ch = var->exp_costs.lca_object.children; (child = *ch); ch++)
    push_stack (nenofex->mm, node_stack, child);

  Node *node;
  while ((node = pop_stack (node_stack)))
    {
      if (is_literal_node (node))
        {                       /* mark variable */
          Var *var = node->lit->var;

          lca_update_mark (var);
          inc_score_update_mark (var);
          dec_score_update_mark (var);
          collect_variable_for_update (nenofex, var);
        }
      else                      /* visit children */
        {
          for (child = node->child_list.first; child;
               child = child->level_link.next)
            push_stack (nenofex->mm, node_stack, child);
        }
    }                           /* end: while stack not empty */
}


/* 
- propagate unate variable by setting value accordingly 
*/
static void
simplify_eliminate_unate (Nenofex * nenofex, Var * var)
{
  assert (variable_has_occs (var));

#if COMPUTE_NUM_UNATES
  nenofex->stats.num_unates++;
#endif

#ifndef NDEBUG
  if (!var->lits[0].occ_list.first)     /* has no neg. occurrences */
    {
      assert (!var->lits[0].occ_list.last);
      assert (var->lits[1].occ_list.first);
      assert (var->lits[1].occ_list.last);
    }
  else                          /* has no pos. occurrences */
    {
      assert (!var->lits[1].occ_list.first);
      assert (!var->lits[1].occ_list.last);
      assert (var->lits[0].occ_list.first);
      assert (var->lits[0].occ_list.last);
    }
#endif

  Lit *lit = !var->lits[0].occ_list.first ? var->lits + 1 : var->lits;
  Node *occ;

  if (is_existential_scope (var->scope))
    {
      while ((occ = lit->occ_list.first))
        {
          propagate_truth (nenofex, occ);
        }
    }
  else                          /* universal variable */
    {
      while ((occ = lit->occ_list.first))
        {
          propagate_falsity (nenofex, occ);
        }
    }

  assert (!variable_has_occs (var));
}


/* 
- search and eliminate unates by checking candidate variables on stack 
- (might also contain variables which have no more occurrences left at all)
*/
static int
simplify_eliminate_unates (Nenofex * nenofex)
{
  Stack *node_stack = 0;

  int found = 0;

  Var *var;
  while ((var = pop_stack (nenofex->unates)))
    {
      assert (var->collected_as_unate);
      var->collected_as_unate = 0;

      if (!variable_has_occs (var))
        {
          var->scope->remaining_var_cnt--;
          assert (var->scope->remaining_var_cnt >= 0);

          if (var->scope->remaining_var_cnt == 0)
            var->scope->is_empty = 1;

          if ((var)->exp_costs.lca_object.lca)
            {
              unlink_variable_from_lca_list (var);
              reset_lca_object (nenofex, var, &(var)->exp_costs.lca_object,
                                1);
            }

          if (var->priority_pos != -1)
            {
              delete_elem_priority_queue (var->scope->priority_heap,
                                          var->priority_pos);
            }

          continue;
        }                       /* end: variable has no occs left */

      assert (var->lits[0].occ_list.first || var->lits[0].occ_cnt == 0);
      assert (var->lits[1].occ_list.first || var->lits[1].occ_cnt == 0);

      Lit *lit = var->lits;
      if (!lit->occ_list.first || !(++lit)->occ_list.first)
        {
          assert (var->lits[0].occ_list.first || !var->lits[0].occ_list.last);
          assert (var->lits[1].occ_list.first || !var->lits[1].occ_list.last);

          if (!node_stack)
            node_stack = create_stack (nenofex->mm, DEFAULT_STACK_SIZE);

          found++;

          if (!var->exp_costs.lca_object.lca || cost_update_marked (var))
            {                   /* re-initialize variable's LCA */
              if ((var)->exp_costs.lca_object.lca)
                {
                  unlink_variable_from_lca_list (var);
                  reset_lca_object (nenofex, var,
                                    &(var)->exp_costs.lca_object, 1);
                }
              find_variable_lca_and_children (nenofex, var,
                                              &var->exp_costs.lca_object, 1);
            }

          assign_or_update_changed_subformula (&(var->exp_costs.lca_object));
          mark_affected_scope_variables_for_cost_update (nenofex,
                                                         var->exp_costs.
                                                         lca_object.lca);
          simplify_mark_lca_variables_for_update (nenofex, var, node_stack);
          simplify_eliminate_unate (nenofex, var);
        }                       /* end: found unate variable */

    }                           /* end: while stack not empty */

  if (node_stack)
    {
      delete_stack (nenofex->mm, node_stack);
      node_stack = 0;
    }

  assert (!node_stack);

  return found;
}


/* 
- immediately conclude falsity
*/
static void
simplify_universal_unit (Nenofex * nenofex)
{
  remove_and_free_subformula (nenofex, nenofex->graph_root);
  assert (nenofex->graph_root == 0);

  nenofex->result = NENOFEX_RESULT_UNSAT;
}


/*
- check root-AND if it has any literal children
- can be done efficiently since by convention lits are stored first in child-list
- NOTE: can check for OR-root as well
*/
static int
simplify_eliminate_units (Nenofex * nenofex)
{
  Node *nenofex_graph_root = nenofex->graph_root;
  Stack *node_stack = 0;
  int found = 0;

  if (!nenofex_graph_root)
    return found;

  if (!is_and_node (nenofex_graph_root))
    return found;

  unsigned int exist_cnt;

  exist_cnt = 0;

  Node *literal = nenofex_graph_root->child_list.first;
  assert (literal);

  if (is_literal_node (literal))
    node_stack = create_stack (nenofex->mm, DEFAULT_STACK_SIZE);

  while (literal && is_literal_node (literal))
    {
#if COMPUTE_NUM_UNITS
      nenofex->stats.num_units++;
#endif

      found = 1;
      Lit *literal_lit = literal->lit;
      Var *var = literal_lit->var;
      Lit *lit = var->lits;

      if (!var->exp_costs.lca_object.lca || cost_update_marked (var))
        {                       /* re-initialize variable's LCA */
          if ((var)->exp_costs.lca_object.lca)
            {
              unlink_variable_from_lca_list (var);
              reset_lca_object (nenofex, var, &(var)->exp_costs.lca_object,
                                1);
            }
          find_variable_lca_and_children (nenofex, var,
                                          &var->exp_costs.lca_object, 1);
        }

      simplify_mark_lca_variables_for_update (nenofex, var, node_stack);

      assign_or_update_changed_subformula (&(var->exp_costs.lca_object));

      if (is_existential_scope (var->scope))
        {
          exist_cnt++;

          if (nenofex->options.show_progress_specified)
            fprintf (stderr, "Found exist. unit literal %d at root-AND\n", var->id);

          if (literal_lit->negated)
            {                   /* eliminate negative unit literal -> set variable to false */
              assert (lit->negated);
              Node *occ;

              while ((occ = lit->occ_list.first))
                {
                  propagate_truth (nenofex, occ);
                }

              lit++;
              assert (!lit->negated);
              while ((occ = lit->occ_list.first))
                {
                  propagate_falsity (nenofex, occ);
                }

              assert (!variable_has_occs (var));
            }
          else
            {                   /* eliminate positive unit literal -> set variable to true */
              assert (lit->negated);
              Node *occ;

              while ((occ = lit->occ_list.first))
                {
                  propagate_falsity (nenofex, occ);
                }

              lit++;
              assert (!lit->negated);
              while ((occ = lit->occ_list.first))
                {
                  propagate_truth (nenofex, occ);
                }

              assert (!variable_has_occs (var));
            }
        }
      else                      /* universal unit literal */
        {
          if (nenofex->options.show_progress_specified)
            fprintf (stderr, "Found univ. unit literal %d at root-AND\n", var->id);
          simplify_universal_unit (nenofex);
          break;
        }

      literal = (nenofex_graph_root = nenofex->graph_root)
        && is_and_node (nenofex_graph_root) ? nenofex_graph_root->child_list.
        first : 0;
    }                           /* end: while unit literals present */

  if (nenofex->options.show_progress_specified && exist_cnt)
    fprintf (stderr, "  Found %d exist. unit literals at root-AND\n",
             exist_cnt);

  if (node_stack)
    {
      delete_stack (nenofex->mm, node_stack);
    }

  return found;
}


/*
- 'changed_subgraph' will become larger if expansions become more costly
- ATPG optimization will have to work on large graph and become VERY expensive
- idea: restrict graph size -> can then be optimized until saturation
- traverses subgraph until child of adequate size found
- collect siblings of this child until size limit reached
*/
static void
reduce_optimization_subgraph_on_demand (Nenofex * nenofex)
{
  unsigned const int size_limit = nenofex->options.opt_subgraph_limit;
  assert (size_limit > 0);

  unsigned int cur_size = 1;

  Node **ch, *child;
  for (ch = nenofex->changed_subformula.children; (child = *ch); ch++)
    cur_size += child->size_subformula;

  if (cur_size <= size_limit)
    return;

  unsigned int max_size = 0;
  Node *max_size_child = 0;

  for (ch = nenofex->changed_subformula.children; (child = *ch); ch++)
    {
      unsigned int child_size_subformula = child->size_subformula;

      if (child_size_subformula > max_size)
        {
          max_size = child_size_subformula;
          max_size_child = child;
        }
    }                           /* end: for all 'changed'-children */

  assert (max_size_child);

  if (max_size > size_limit)
    {                           /* continue search at max_size_child's children */
      Node *first_child;

    AGAIN:

      first_child = max_size_child->child_list.first;
      max_size_child = 0;
      max_size = 0;

      for (child = first_child; child; child = child->level_link.next)
        {
          unsigned int child_size_subformula = child->size_subformula;

          if (child_size_subformula > max_size)
            {
              max_size = child_size_subformula;
              max_size_child = child;
            }
        }                       /* end: for all max_size_child's children */

      if (max_size > size_limit)
        goto AGAIN;
    }                           /* end: continue search */

  reset_changed_lca_object (nenofex);

  if (!max_size_child
      || (!MAXIMIZE_REDUCED && is_literal_node (max_size_child)))
    return;

  unsigned int reduced_size = max_size_child->size_subformula;

#if MAXIMIZE_REDUCED
  nenofex->changed_subformula.lca = max_size_child->parent;
  reduced_size++;
  add_changed_lca_child (nenofex, max_size_child);

  child = max_size_child->level_link.next;
  if (!child)
    child = max_size_child->parent->child_list.first;

  for (; child != max_size_child;
       child = (child->level_link.next ? child->level_link.next :
                max_size_child->parent->child_list.first))
    {
      if (reduced_size + child->size_subformula <= size_limit)
        {
          reduced_size += child->size_subformula;
          add_changed_lca_child (nenofex, child);
        }
    }                           /* end: for all childlen */

  if (nenofex->changed_subformula.num_children == 1)
    reset_changed_lca_object (nenofex);
#endif

  /* assign new 'changed_subformula ' */

  if (nenofex->changed_subformula.num_children == 0)
    {
      nenofex->changed_subformula.lca = max_size_child;

      for (child = max_size_child->child_list.first;
           child; child = child->level_link.next)
        add_changed_lca_child (nenofex, child);
    }
#ifndef NDEBUG
#if ASSERT_POS_IN_CHANGED_CH_LIST
  assert_pos_in_changed_ch_list (nenofex);
#endif
#endif

  if (nenofex->options.show_progress_specified)
    fprintf (stderr, "Reduced 'Changed-Subgraph' from size %d to size %d\n\n",
             cur_size, reduced_size);
}


static int
simplify_by_global_flow_and_atpg (Nenofex * nenofex)
{
  int graph_modified = 0;

  if (nenofex->changed_subformula.lca)
    {
      if (nenofex->options.opt_subgraph_limit_specified)
        {
          reduce_optimization_subgraph_on_demand (nenofex);

          if (!nenofex->changed_subformula.lca)
            return 0;
        }

      graph_modified = simplify_by_global_flow_and_atpg_main (nenofex);
    }

  return graph_modified;
}


#ifndef NDEBUG
/*
- for assertion checking only
- assert: vars in non-innermost scopes either eliminated (e.g. unates) or costs uninitialized
*/
static void
assert_all_non_innermost_scope_vars_uninitialized (Nenofex * nenofex,
                                                   Scope ** scope)
{
  assert (*scope == find_innermost_non_empty_scope (nenofex));
  scope--;                      /* 'scope' pointed to current scope before */

  void **v_scope, **scope_start;
  scope_start = nenofex->scopes->elems;
  for (v_scope = (void **) scope; v_scope >= scope_start; v_scope--)
    {
      Scope *scope = *v_scope;

      void **v_var;
      for (v_var = scope->vars->top - 1; v_var >= scope->vars->elems; v_var--)
        {
          Var *var = *v_var;
          assert (!variable_has_occs (var) || !var->exp_costs.lca_object.lca
                  || var->scope == *nenofex->next_scope);
        }                       /* end: for all vars in scope */

    }                           /* end: for all scopes */
}
#endif


/* 
- compute graph statistics via full traversal of graph 
- rather expensive
- NOTE: this could also be done incrementally 
*/
static void
compute_graph_statistics (Nenofex * nenofex)
{
/* node count*/
  unsigned int lit_node_cnt = 0;
  unsigned int and_node_cnt = 0;
  unsigned int or_node_cnt = 0;
  unsigned int op_node_cnt = 0;
  unsigned int node_cnt = 0;

/* literal-child count */
  unsigned int max_lit_cnt_per_or_node = 0;
  unsigned int total_lit_cnt_per_or_node = 0;
  float average_lit_cnt_per_or_node = 0;

  unsigned int max_lit_cnt_per_and_node = 0;
  unsigned int total_lit_cnt_per_and_node = 0;
  float average_lit_cnt_per_and_node = 0;

  unsigned int max_lit_cnt_per_op_node = 0;
  unsigned int total_lit_cnt_per_op_node = 0;
  float average_lit_cnt_per_op_node = 0;

/* arity */
  unsigned int max_or_node_arity = 0;
  unsigned int total_or_node_arity = 0;
  float average_arity_per_or_node = 0;

  unsigned int max_and_node_arity = 0;
  unsigned int total_and_node_arity = 0;
  float average_arity_per_and_node = 0;

  unsigned int max_op_node_arity = 0;
  unsigned int total_op_node_arity = 0;
  float average_arity_per_op_node = 0;

/* level */
  unsigned int max_or_node_level = 0;
  unsigned int total_or_node_level = 0;
  float average_level_per_or_node = 0;

  unsigned int max_and_node_level = 0;
  unsigned int total_and_node_level = 0;
  float average_level_per_and_node = 0;

  unsigned int max_lit_node_level = 0;
  unsigned int total_lit_node_level = 0;
  float average_level_per_lit_node = 0;

  unsigned int max_node_level = 0;
  unsigned int total_node_level = 0;
  float average_level_per_node = 0;

  Stack *stack = create_stack (nenofex->mm, DEFAULT_STACK_SIZE);
  push_stack (nenofex->mm, stack, nenofex->graph_root);

  Node *cur;
  while ((cur = pop_stack (stack)))
    {
      if (is_literal_node (cur))
        {
          lit_node_cnt++;
          total_lit_node_level += cur->level;

          if (cur->level > max_lit_node_level)
            max_lit_node_level = cur->level;
        }
      else                      /* operator node */
        {
          if (is_or_node (cur))
            {
              or_node_cnt++;
              total_or_node_arity += cur->num_children;

              if (cur->num_children > max_or_node_arity)
                max_or_node_arity = cur->num_children;

              total_or_node_level += cur->level;

              if (cur->level > max_or_node_level)
                max_or_node_level = cur->level;

              Node *ch;
              unsigned int cur_lit_cnt = 0;
              for (ch = cur->child_list.last; ch; ch = ch->level_link.prev)
                {
                  if (is_literal_node (ch))
                    {
                      cur_lit_cnt++;
                      total_lit_cnt_per_or_node++;
                    }
                  push_stack (nenofex->mm, stack, ch);
                }               /* end: for all children */

              if (cur_lit_cnt > max_lit_cnt_per_or_node)
                max_lit_cnt_per_or_node = cur_lit_cnt;
            }
          else                  /* and */
            {
              and_node_cnt++;
              total_and_node_arity += cur->num_children;

              if (cur->num_children > max_and_node_arity)
                max_and_node_arity = cur->num_children;

              total_and_node_level += cur->level;

              if (cur->level > max_and_node_level)
                max_and_node_level = cur->level;

              Node *ch;
              unsigned int cur_lit_cnt = 0;
              for (ch = cur->child_list.last; ch; ch = ch->level_link.prev)
                {
                  if (is_literal_node (ch))
                    {
                      cur_lit_cnt++;
                      total_lit_cnt_per_and_node++;
                    }
                  push_stack (nenofex->mm, stack, ch);
                }               /* end: for all children */

              if (cur_lit_cnt > max_lit_cnt_per_and_node)
                max_lit_cnt_per_and_node = cur_lit_cnt;

            }                   /* end: and */
        }                       /* end: op-node */

    }                           /* end: while stack not empty */

  op_node_cnt = or_node_cnt + and_node_cnt;
  node_cnt = op_node_cnt + lit_node_cnt;
  assert (node_cnt == nenofex->graph_root->size_subformula);

  max_lit_cnt_per_op_node =
    (max_lit_cnt_per_or_node >
     max_lit_cnt_per_and_node) ? max_lit_cnt_per_or_node :
    max_lit_cnt_per_and_node;
  total_lit_cnt_per_op_node =
    total_lit_cnt_per_or_node + total_lit_cnt_per_and_node;
  average_lit_cnt_per_op_node =
    (float) total_lit_cnt_per_op_node / op_node_cnt;
  average_lit_cnt_per_or_node =
    (float) total_lit_cnt_per_or_node / or_node_cnt;
  average_lit_cnt_per_and_node =
    (float) total_lit_cnt_per_and_node / and_node_cnt;


  max_op_node_arity = (max_or_node_arity > max_and_node_arity) ?
    max_or_node_arity : max_and_node_arity;
  total_op_node_arity = total_or_node_arity + total_and_node_arity;
  average_arity_per_op_node = (float) total_op_node_arity / op_node_cnt;
  average_arity_per_or_node = (float) total_or_node_arity / or_node_cnt;
  average_arity_per_and_node = (float) total_and_node_arity / and_node_cnt;

  total_node_level =
    total_lit_node_level + total_or_node_level + total_and_node_level;
  max_node_level =
    (max_lit_node_level >
     max_or_node_level) ? max_lit_node_level : max_or_node_level;
  max_node_level =
    (max_node_level >
     max_and_node_level) ? max_node_level : max_and_node_level;

  average_level_per_node = (float) total_node_level / node_cnt;
  average_level_per_lit_node = (float) total_lit_node_level / lit_node_cnt;
  average_level_per_or_node = (float) total_or_node_level / or_node_cnt;
  average_level_per_and_node = (float) total_and_node_level / and_node_cnt;

  FILE *out = stderr;

  fprintf (out, "NODE COUNT:\n");
  fprintf (out, "\ttotal node count: %d\n", node_cnt);
  fprintf (out, "\ttotal op node count: %d\n", op_node_cnt);
  fprintf (out, "\ttotal or node count: %d\n", or_node_cnt);
  fprintf (out, "\ttotal and node count: %d\n", and_node_cnt);
  fprintf (out, "\ttotal lit node count: %d\n", lit_node_cnt);
  fprintf (out, "--\n");

  fprintf (out, "LITERAL-CHILD COUNT:\n");
  fprintf (out, "\tmax lit count per or node: %d\n", max_lit_cnt_per_or_node);
  fprintf (out, "\tmax lit count per and node: %d\n",
           max_lit_cnt_per_and_node);
  fprintf (out, "\tmax lit count per op node: %d\n", max_lit_cnt_per_op_node);
  fprintf (out, "\taverage lit count per or node: %f\n",
           average_lit_cnt_per_or_node);
  fprintf (out, "\taverage lit count per and node: %f\n",
           average_lit_cnt_per_and_node);
  fprintf (out, "\taverage lit count per op node: %f\n",
           average_lit_cnt_per_op_node);
  fprintf (out, "--\n");

  fprintf (out, "ARITY:\n");
  fprintf (out, "\tmax or node arity: %d\n", max_or_node_arity);
  fprintf (out, "\tmax and node arity : %d\n", max_and_node_arity);
  fprintf (out, "\tmax op node arity: %d\n", max_op_node_arity);
  fprintf (out, "\taverage arity per or node: %f\n",
           average_arity_per_or_node);
  fprintf (out, "\taverage arity per and node: %f\n",
           average_arity_per_and_node);
  fprintf (out, "\taverage arity per op node: %f\n",
           average_arity_per_op_node);
  fprintf (out, "--\n");

  fprintf (out, "LEVEL:\n");
  fprintf (out, "\tmax or node level: %d\n", max_or_node_level);
  fprintf (out, "\tmax and node level: %d\n", max_and_node_level);
  fprintf (out, "\tmax lit node level: %d\n", max_lit_node_level);
  fprintf (out, "\tmax node level: %d\n", max_node_level);
  fprintf (out, "\taverage level per or node: %f\n",
           average_level_per_or_node);
  fprintf (out, "\taverage level per and node: %f\n",
           average_level_per_and_node);
  fprintf (out, "\taverage level per lit node: %f\n",
           average_level_per_lit_node);
  fprintf (out, "\taverage level per node: %f\n", average_level_per_node);
  fprintf (out, "--\n");

  delete_stack (nenofex->mm, stack);
}


#if APPROXIMATE_UNIV_SCORES
/*
- initialize all variables in a scope from scratch
- priority order has to be established manually afetrwards by calling 'init_order'
*/
static void
approximate_univ_scope_variable_scores (Nenofex * nenofex, Scope * scope)
{
  void **v_var, **end;
  end = scope->vars->top;

  unsigned int lits = 0, min_lits = UINT_MAX;
  Var *min_lit_var = 0;

  for (v_var = scope->vars->elems; v_var < end; v_var++)
    {
      Var *var = *v_var;

      if ((lits = (var->lits[0].occ_cnt + var->lits[1].occ_cnt)) > 0
          && lits < min_lits)
        {
          min_lits = lits;
          min_lit_var = var;
        }

      lca_update_unmark (var);
      inc_score_update_unmark (var);
      dec_score_update_unmark (var);
    }                           /* end: for all vars in scope */

  if (!min_lit_var)             /* empty scope */
    return;

  lca_update_mark (min_lit_var);
  inc_score_update_mark (min_lit_var);
  dec_score_update_mark (min_lit_var);

  init_variable_scores (nenofex, min_lit_var, 0);

  lca_update_unmark (min_lit_var);
  inc_score_update_unmark (min_lit_var);
  dec_score_update_unmark (min_lit_var);

  for (v_var = scope->vars->elems; v_var < end; v_var++)
    {
      Var *var = *v_var;
      if (var != min_lit_var)
        {
          var->exp_costs.score = min_lit_var->exp_costs.score + 1;
          var->exp_costs.inc_score = var->exp_costs.score;
          var->exp_costs.dec_score = 0;
        }
    }
}
#endif

/*
- initialize all variables in a scope from scratch
- priority order has to be established manually afetrwards by calling 'init_order'
*/
static void
init_all_scope_variable_scores (Nenofex * nenofex, Scope * scope)
{
#if APPROXIMATE_UNIV_SCORES
  if (nenofex->consider_univ_exp && nenofex->cur_scope
      && is_existential_scope (*nenofex->cur_scope) && nenofex->next_scope
      && is_universal_scope (*nenofex->next_scope))
    {
      approximate_univ_scope_variable_scores (nenofex, scope);
      return;
    }
#endif

  void **v_var, **end;
  end = scope->vars->top;

  for (v_var = scope->vars->elems; v_var < end; v_var++)
    {
      Var *var = *v_var;

      lca_update_mark (var);
      inc_score_update_mark (var);
      dec_score_update_mark (var);

      init_variable_scores (nenofex, var, 0);

      lca_update_unmark (var);
      inc_score_update_unmark (var);
      dec_score_update_unmark (var);
    }                           /* end: for all vars in scope */
}


/*
- find cheapest univrsal variable from non-innermost universal scope
- actually called only after prior call of 'peek_min_cost_universal_var_in_next_scope'
*/
static Var *
find_min_cost_universal_var_in_next_scope (Nenofex * nenofex,
                                           Scope * universal_scope,
                                           const int init_scope_vars)
{
  assert (is_universal_scope (universal_scope));
  assert (universal_scope == *nenofex->next_scope);
  assert (is_existential_scope (*nenofex->cur_scope));

  if (init_scope_vars)
    {                           /* NOTE: rather expensive */
      if (nenofex->options.show_progress_specified)
        fprintf (stderr, "Initializing non-innermost universal scope...\n");
      init_all_scope_variable_scores (nenofex, universal_scope);
      init_order_priority_queue (universal_scope->priority_heap);
    }

  if (nenofex->options.show_progress_specified)
    fprintf (stderr, "\thas total %d variables, remaining %d\n",
             count_stack (universal_scope->vars),
             count_stack (universal_scope->priority_heap));

  Var *min_cost_var = 0;
  Stack *scope_priority_heap = universal_scope->priority_heap;

  while ((min_cost_var = remove_min (scope_priority_heap)))
    {
      if (variable_has_occs (min_cost_var))
        break;
      else
        {
          assert (0);
        }
    }

  nenofex->num_cur_remaining_scope_vars = count_stack (scope_priority_heap);

  if (min_cost_var && nenofex->options.show_progress_specified)
    fprintf (stderr, "\tfound non-innermost univ. var %d with cost %d\n",
             min_cost_var->id, min_cost_var->exp_costs.score);

  return min_cost_var;
}


/*
- like 'find_min_cost_universal_var_in_next_scope' but does not remove var from p.queue
*/
static Var *
peek_min_cost_universal_var_in_next_scope (Nenofex * nenofex,
                                           Scope * universal_scope,
                                           const int init_scope_vars)
{
  assert (is_universal_scope (universal_scope));
  assert (universal_scope == (*nenofex->next_scope));
  assert (is_existential_scope (*nenofex->cur_scope));

  if (init_scope_vars)
    {                           /* NOTE: rather expensive */
      if (nenofex->options.show_progress_specified)
        fprintf (stderr, "Initializing non-innermost universal scope...\n");
      init_all_scope_variable_scores (nenofex, universal_scope);
      init_order_priority_queue (universal_scope->priority_heap);
    }

  Var *min_cost_var = 0;
  Stack *scope_priority_heap = universal_scope->priority_heap;

  while ((min_cost_var = access_min (scope_priority_heap)))
    {
      if (variable_has_occs (min_cost_var))
        break;
      else
        {
          assert (0);
        }
    }

  return min_cost_var;
}


static void
copy_and_add_depending_variable (Nenofex * nenofex, Var * depending_var)
{
  Var *var_copy = (Var *) mem_malloc (nenofex->mm, sizeof (Var));
  assert (var_copy);
  memset (var_copy, 0, sizeof (Var));

  var_copy->pos_in_lca_child_list_occs = create_stack (nenofex->mm, DEFAULT_STACK_SIZE);

  var_copy->exp_costs.score = INT_MIN;

  init_lca_object (nenofex, &(var_copy->exp_costs.lca_object));

  var_copy->id = depending_var->id;     /* var-IDs do not matter at all */
  var_copy->priority_pos = -1;
  var_copy->lits[0].var = var_copy;
  var_copy->lits[0].negated = 1;
  var_copy->lits[1].var = var_copy;
  var_copy->lits[1].negated = 0;
  var_copy->lits[0].occ_list.first = (Node *) 0;
  var_copy->lits[0].occ_list.last = (Node *) 0;
  var_copy->lits[1].occ_list.first = (Node *) 0;
  var_copy->lits[1].occ_list.last = (Node *) 0;

  Scope *scope = depending_var->scope;
  push_stack (nenofex->mm, scope->vars, var_copy);
  scope->remaining_var_cnt++;

  add_fast_priority_queue (nenofex->mm, scope->priority_heap, var_copy);

  var_copy->scope = scope;

  depending_var->copied = var_copy;

  collect_variable_as_unate (nenofex, var_copy);

  /* copied variables' scores will have to be updated before next expansion */
  lca_update_mark (var_copy);
  inc_score_update_mark (var_copy);
  dec_score_update_mark (var_copy);
  collect_variable_for_update (nenofex, var_copy);
}


static void
copy_innermost_depending_existential_variables (Nenofex * nenofex)
{
  void **v_var, **end;
  end = nenofex->depending_vars->top;

  for (v_var = nenofex->depending_vars->elems; v_var < end; v_var++)
    {
      Var *var = *v_var;
      assert (var->collected_as_depending);
      assert (is_existential_scope (var->scope));
      assert (var->scope == (*nenofex->cur_scope));
      assert (!var->copied);

      copy_and_add_depending_variable (nenofex, var);

      /* depending variables' scores will be updated before next expansion */
      lca_update_mark (var);
      inc_score_update_mark (var);
      dec_score_update_mark (var);
      collect_variable_for_update (nenofex, var);
    }                           /* end: for all depending variables */

  /* TODO: avoid complete recalculation of order */
  init_order_priority_queue ((*nenofex->cur_scope)->priority_heap);
}


/*
- must be called before a universal variable from non-innermost scope is expanded
- collect and copy depending existential variables
- NOTE: set of depending vars is known after LCA-computation -> need not recompute 
*/
static void
prepare_non_innermost_universal_expansion (Nenofex * nenofex,
                                           Var * universal_var)
{
  assert (is_universal_scope (universal_var->scope));
  assert (universal_var->scope == *nenofex->next_scope);
  assert (!count_stack (nenofex->depending_vars));
#ifndef NDEBUG
#if ASSERT_PREPARE_NON_INNERMOST_UNIVERSAL_EXPANSION
  assert_no_var_collected_as_depending (nenofex);
#endif
#endif

  /* TODO: not necessary if depending vars are stored after LCA computation */
  collect_innermost_depending_existential_variables (nenofex, universal_var,
                                                     nenofex->depending_vars,
                                                     0);

  if (nenofex->options.show_progress_specified)
    fprintf (stderr, "\tvar. has %d depending existential variables\n",
             count_stack (nenofex->depending_vars));

  copy_innermost_depending_existential_variables (nenofex);
}


/*
- compute scores of variables which have been collected for update
*/
static void
collected_variables_update_scores (Nenofex * nenofex)
{
#if (PRINT_INCREMENTAL_COST_UPDATE || COMPUTE_AVERAGE_UPDATE_MARKED_RATIOS)
  unsigned int cnt_update_lca = 0;
  unsigned int cnt_update_inc_score = 0;
  unsigned int cnt_update_dec_score = 0;
#endif

  Stack *collected_variables = nenofex->vars_marked_for_update;

  Var *update_var;
  while ((update_var = pop_stack (collected_variables)))
    {
      assert (update_var->collected_for_update);
      assert (update_var->scope == *nenofex->cur_scope);

      update_var->collected_for_update = 0;

      if (!cost_update_marked (update_var))
        continue;

      if (variable_has_occs (update_var))
        {                       /* update */
          init_variable_scores (nenofex, update_var, 1);

#if (PRINT_INCREMENTAL_COST_UPDATE || COMPUTE_AVERAGE_UPDATE_MARKED_RATIOS)
          if (lca_update_marked (update_var))
            cnt_update_lca++;
          if (inc_score_update_marked (update_var))
            cnt_update_inc_score++;
          if (dec_score_update_marked (update_var))
            cnt_update_dec_score++;
#endif
        }

      lca_update_unmark (update_var);
      inc_score_update_unmark (update_var);
      dec_score_update_unmark (update_var);
    }                           /* end: for all marked variables */

#if PRINT_INCREMENTAL_COST_UPDATE
  fprintf (stderr,
           "Found %d vars lca-marked from %d vars remaining in scope\n",
           cnt_update_lca,
           count_stack ((*nenofex->cur_scope)->priority_heap));
  fprintf (stderr,
           "Found %d vars inc_score-marked from %d vars remaining in scope\n",
           cnt_update_inc_score,
           count_stack ((*nenofex->cur_scope)->priority_heap));
  fprintf (stderr,
           "Found %d vars dec_score-marked from %d vars remaining in scope\n",
           cnt_update_dec_score,
           count_stack ((*nenofex->cur_scope)->priority_heap));
#endif

#if COMPUTE_AVERAGE_UPDATE_MARKED_RATIOS
  unsigned int remaining = count_stack ((*nenofex->cur_scope)->priority_heap);
  nenofex->stats.sum_remaining += remaining;
  if (remaining == 0)
    remaining = 1;
  nenofex->stats.sum_lca_marked += cnt_update_lca;
  nenofex->stats.sum_inc_marked += cnt_update_inc_score;
  nenofex->stats.sum_dec_marked += cnt_update_dec_score;
  nenofex->stats.sum_ratio_lca_marked_in_scope_vars +=
    ((double) cnt_update_lca / remaining);
  nenofex->stats.sum_ratio_inc_marked_in_scope_vars +=
    ((double) cnt_update_inc_score / remaining);
  nenofex->stats.sum_ratio_dec_marked_in_scope_vars +=
    ((double) cnt_update_dec_score / remaining);
#endif
}


#define move_scope(scope, scopes_start) \
if (scope) \
{ \
  assert(scope >= (Scope **) scopes_start); \
  while(scope > (Scope **) scopes_start) \
  { \
    scope--; \
    if (!is_empty_scope(nenofex, *scope)) \
      break; \
    else \
    (*scope)->is_empty = 1; \
  } \
  if (scope == (Scope **) scopes_start) \
    scope = 0; \
}


/*
- possible situation: 'next_scope' and 'cur_scope' are both of the same kind
- may happen if the scope between has become empty
- merge 'next_scope' and 'cur_scope' scope into one and find new 'next_scope'
*/
static void
merge_cur_and_next_scope (Nenofex * nenofex)
{
AGAIN:

  assert (nenofex->cur_scope);
  assert (nenofex->next_scope);

  Scope *cur_scope = *nenofex->cur_scope;
  Scope *next_scope = *nenofex->next_scope;
  assert (cur_scope->type == next_scope->type);

  if (nenofex->options.show_progress_specified)
    fprintf (stderr, "Merging scopes %d and %d...\n",
             next_scope->nesting, cur_scope->nesting);

  Stack *cur_scope_vars = cur_scope->vars;
  Stack *next_scope_vars = next_scope->vars;

  next_scope->remaining_var_cnt += cur_scope->remaining_var_cnt;
  cur_scope->remaining_var_cnt = 0;

  Var *var;
  while ((var = pop_stack (cur_scope_vars)))
    {                           /* move vars from 'cur_scope' to 'next_scope' scope */
      var->exp_costs.score = INT_MIN;

      if (var->exp_costs.lca_object.lca)
        {
          unlink_variable_from_lca_list (var);
          reset_lca_object (nenofex, var, &(var)->exp_costs.lca_object, 1);
        }

      var->priority_pos = -1;
      push_stack (nenofex->mm, next_scope_vars, var);
      var->scope = next_scope;

      if (variable_has_occs (var))
        add_fast_priority_queue (nenofex->mm, next_scope->priority_heap, var);
    }                           /* end: for all variables in 'cur_scope' */

  reset_stack (cur_scope->priority_heap);
  cur_scope->is_empty = 1;

  /* initialize 'next_scope' from scratch */
  init_all_scope_variable_scores (nenofex, next_scope);
  init_order_priority_queue (next_scope->priority_heap);

  /* find new 'next_scope' */
  nenofex->cur_scope = nenofex->next_scope;
  move_scope (nenofex->next_scope, nenofex->scopes->elems);

  if (nenofex->next_scope &&
      (*nenofex->next_scope)->type == (*nenofex->cur_scope)->type)
    goto AGAIN;
}


/*
- expand either the cheapest exist. var from innermost scope or a univ. var from next scope
- pointers to 'next_scope' and 'cur_scope' are maintained
- a scope is moved to the next outer scope if it becomes empty
- if 'next_scope' and 'cur_scope' are both of the same 
   type they will be merged into one scope
*/
static Var *
pick_variable_for_expansion (Nenofex * nenofex)
{
  assert (nenofex->cur_scope);
  assert (!nenofex->next_scope ||
          (*nenofex->next_scope)->type != (*nenofex->cur_scope)->type);

  collected_variables_update_scores (nenofex);

  assert (!nenofex->consider_univ_exp || nenofex->next_scope);
  assert (!nenofex->consider_univ_exp || !nenofex->next_scope ||
          (is_existential_scope (*nenofex->cur_scope) &&
           is_universal_scope (*nenofex->next_scope)));

  Var *min_var = 0, *min_cur_scope_var = 0, *min_next_scope_var = 0;

  min_cur_scope_var =
    peek_min_cost_var_in_scope (nenofex, *nenofex->cur_scope);

  if (!min_cur_scope_var)
    {                           /* cur. scope is empty -> move both next and cur. scope */
      (*nenofex->cur_scope)->is_empty = 1;
      assert (is_empty_scope (nenofex, *nenofex->cur_scope));

      move_scope (nenofex->next_scope, nenofex->scopes->elems);
      move_scope (nenofex->cur_scope, nenofex->scopes->elems);

      assert (nenofex->cur_scope
              && nenofex->cur_scope > (Scope **) nenofex->scopes->elems);

      /* both scopes were empty */
      if (nenofex->cur_scope == nenofex->next_scope)
        move_scope (nenofex->next_scope, nenofex->scopes->elems);

      if (nenofex->next_scope &&
          (*nenofex->next_scope)->type == (*nenofex->cur_scope)->type)
        {                       /* merge scopes */
          merge_cur_and_next_scope (nenofex);
        }

      assert (!nenofex->next_scope ||
              nenofex->next_scope > (Scope **) nenofex->scopes->elems);

      /* initialize cur. scope */
      init_all_scope_variable_scores (nenofex, *nenofex->cur_scope);
      init_order_priority_queue ((*nenofex->cur_scope)->priority_heap);

      if (!nenofex->next_scope
          || (is_existential_scope (*nenofex->next_scope)
              && is_universal_scope (*nenofex->cur_scope)))
        nenofex->consider_univ_exp = 0;

      min_cur_scope_var =
        peek_min_cost_var_in_scope (nenofex, *nenofex->cur_scope);
    }                           /* end: cur. scope is empty */
  assert (min_cur_scope_var);

  if (nenofex->next_scope)
    {

      if (nenofex->consider_univ_exp
          && is_universal_scope (*nenofex->next_scope)
          && is_existential_scope (*nenofex->cur_scope))
        {                       /* next scope is univ., cur is exist. -> pick variable on demand only (expensive score comp.) */
          min_next_scope_var =
            peek_min_cost_universal_var_in_next_scope (nenofex,
                                                       *nenofex->next_scope,
                                                       1);

          if (!min_next_scope_var)
            {                   /* next scope is empty */
              (*nenofex->next_scope)->is_empty = 1;
              assert (is_empty_scope (nenofex, *nenofex->next_scope));

              move_scope (nenofex->next_scope, nenofex->scopes->elems);

              if (nenofex->next_scope &&
                  (*nenofex->next_scope)->type == (*nenofex->cur_scope)->type)
                {               /* merge scopes */
                  merge_cur_and_next_scope (nenofex);
                }

              assert (!nenofex->next_scope ||
                      nenofex->next_scope >
                      (Scope **) nenofex->scopes->elems);
              assert (!nenofex->next_scope
                      || (is_universal_scope (*nenofex->next_scope)
                          && is_existential_scope (*nenofex->cur_scope)));

              if (nenofex->next_scope)
                min_next_scope_var =
                  peek_min_cost_universal_var_in_next_scope (nenofex,
                                                             *nenofex->
                                                             next_scope, 1);
              else
                nenofex->consider_univ_exp = 0;
            }
        }                       /* end: possible non-innermost universal expansion */
    }                           /* end: next scope exists */

  if (nenofex->consider_univ_exp && min_next_scope_var)
    {                           /* if univ. expansion enabled, then expand regardless of cheapest exist. var. */
      assert (is_universal_scope (*nenofex->next_scope) &&
              is_existential_scope (*nenofex->cur_scope));
      min_var =
        find_min_cost_universal_var_in_next_scope (nenofex,
                                                   *nenofex->next_scope, 0);
      prepare_non_innermost_universal_expansion (nenofex, min_var);
      nenofex->consider_univ_exp = 0;
    }
  else
    {
      min_var = find_min_cost_var_in_scope (nenofex, *nenofex->cur_scope);
    }

  assert (min_var);
  assert (!nenofex->consider_univ_exp);
  assert (!nenofex->next_scope ||
          (*nenofex->next_scope)->type != (*nenofex->cur_scope)->type);

  return min_var;
}


#ifndef NDEBUG
static void
assert_all_scope_variable_counts (Nenofex * nenofex)
{
  void **v_scope, **scope_end;
  scope_end = nenofex->scopes->top;
  for (v_scope = nenofex->scopes->elems; v_scope < scope_end; v_scope++)
    {
      Scope *scope = *v_scope;
      int remaining = 0;
      void **v_var, **var_end;
      var_end = scope->vars->top;
      for (v_var = scope->vars->elems; v_var < var_end; v_var++)
        {
          Var *var = *v_var;
          if (variable_has_occs (var))
            remaining++;
        }                       /* end: for all vars in scope */

      assert (remaining == scope->remaining_var_cnt);
    }                           /* end: for all scopes */
}
#endif


#ifndef NDEBUG
static void
assert_all_scopes_free_of_no_occ_vars (Nenofex * nenofex)
{
  void **v_scope, **scope_end;
  scope_end = nenofex->scopes->top;
  for (v_scope = nenofex->scopes->elems; v_scope < scope_end; v_scope++)
    {
      Scope *scope = *v_scope;
      void **v_var, **var_end;
      var_end = scope->priority_heap->top;
      for (v_var = scope->priority_heap->elems; v_var < var_end; v_var++)
        {
          Var *var = *v_var;
          assert (variable_has_occs (var));
        }                       /* end: for all vars in scope */
    }                           /* end: for all scopes */
}
#endif


#ifndef NDEBUG
static void
assert_all_scopes_priority_queue_heap_condition (Nenofex * nenofex)
{
  void **v_scope, **scope_end;
  scope_end = nenofex->scopes->top;
  for (v_scope = nenofex->scopes->elems; v_scope < scope_end; v_scope++)
    {
      Scope *scope = *v_scope;
      assert_priority_queue_heap_condition (scope->priority_heap);
    }                           /* end: for all scopes */
}
#endif


static void
print_lit_stats_before_exp (Nenofex * nenofex, Var * var)
{
#if 1
  if (var->exp_costs.score <= 50)
    return;
#endif

  int neg_lit_count = 0;
  int pos_lit_count = 0;

  Lit *lit = var->lits;
  Node *lit_node;
  for (lit_node = lit->occ_list.first; lit_node;
       lit_node = lit_node->occ_link.next)
    neg_lit_count++;

  lit++;
  for (lit_node = lit->occ_list.first; lit_node;
       lit_node = lit_node->occ_link.next)
    pos_lit_count++;

  /* Estimate how many nodes could be shared. This is done by detecting 
     which subtrees' functions are not affected by expansion. */
  LCAObject *lcaobj = &var->exp_costs.lca_object;
  Stack *stack = create_stack (nenofex->mm, 1);
  Node **childpp, *childp, *tmp;

#ifndef NDEBUG
#if ASSERT_PRINT_LIT_STATS_BEFORE_EXP
  /* Make sure that no node is marked. */
  assert (count_stack (stack) == 0);
  do
    {
      for (childpp = lcaobj->children; (childp = *childpp); childpp++)
        push_stack (nenofex->mm, stack, childp);

      while ((childp = pop_stack (stack)))
        {
          assert (!childp->mark1);
          for (childp = childp->child_list.first; childp;
               childp = childp->level_link.next)
            push_stack (nenofex->mm, stack, childp);
        }
    }
  while (0);
#endif
#endif


  /* Mark ancestors of literals up to LCA. */
  lit = var->lits;
  for (lit_node = lit->occ_list.first; lit_node;
       lit_node = lit_node->occ_link.next)
    {
      tmp = lit_node;
      do
        {
          tmp->mark1 = 1;
          tmp = tmp->parent;
        }
      while (tmp && tmp->level >= lcaobj->lca->level);
    }

  lit++;
  for (lit_node = lit->occ_list.first; lit_node;
       lit_node = lit_node->occ_link.next)
    {
      tmp = lit_node;
      do
        {
          tmp->mark1 = 1;
          tmp = tmp->parent;
        }
      while (tmp && tmp->level >= lcaobj->lca->level);
    }

  unsigned int total_size = 0;
  assert (lcaobj->lca->mark1);

  /* Traverse LCA-subtree and count subtree sizes. */
  assert (count_stack (stack) == 0);
  for (childpp = lcaobj->children; (childp = *childpp); childpp++)
    push_stack (nenofex->mm, stack, childp);

  while ((childp = pop_stack (stack)))
    {

      if (!childp->mark1)
        {
          total_size = childp->size_subformula;
        }
      else
        {
          childp->mark1 = 0;
          for (childp = childp->child_list.first; childp;
               childp = childp->level_link.next)
            push_stack (nenofex->mm, stack, childp);
        }
    }

#ifndef NDEBUG
#if ASSERT_PRINT_LIT_STATS_BEFORE_EXP
  /* Make sure that no node is marked. */
  assert (count_stack (stack) == 0);
  do
    {
      for (childpp = lcaobj->children; (childp = *childpp); childpp++)
        push_stack (stack, childp);

      while ((childp = pop_stack (stack)))
        {
          assert (!childp->mark1);
          for (childp = childp->child_list.first; childp;
               childp = childp->level_link.next)
            push_stack (stack, childp);
        }
    }
  while (0);
#endif
#endif

  delete_stack (nenofex->mm, stack);

  fprintf (stderr, "\nBEFORE INNERMOST EXP: LIT STATS\n");

  fprintf (stderr,
           "Var %d has %d neg. lits, %d pos. lits and total %d lits\n",
           var->id, neg_lit_count, pos_lit_count,
           neg_lit_count + pos_lit_count);

  fprintf (stderr, "Var %d has %d inc-score, %d dec-score, %d total-score\n",
           var->id, var->exp_costs.inc_score, var->exp_costs.dec_score,
           var->exp_costs.inc_score - var->exp_costs.dec_score);

  fprintf (stderr,
           "Var %d summary: %d total-lits, %d total-cost, %d sharing-potential\n\n",
           var->id, neg_lit_count + pos_lit_count,
           var->exp_costs.inc_score - var->exp_costs.dec_score, total_size);

}


/*
- core function: eliminate vars from innermost scope based on expansion costs
- abort according to specified options or if result is known
- NEW: expansion of univ. var. from non-innermost scope (must be enabled first)
*/
static void
expansion_phase (Nenofex * nenofex)
{
  assert (!nenofex->is_existential);
  assert (!nenofex->is_universal);
  assert (!nenofex->consider_univ_exp);
  assert (((Scope *) * nenofex->scopes->elems)->nesting ==
          DEFAULT_SCOPE_NESTING);

  /* Store graph size at start of expansion phase. */
  nenofex->init_graph_size = nenofex->graph_root ? 
    nenofex->graph_root->size_subformula : 0;

#if 1                           /* WORKAROUND: remove vars without any occs after parsing 
                                   (violation of QDIMACS standard) */
  simplify_eliminate_unates (nenofex);
#endif

  Var *var = 0;
  nenofex->cur_scope = (Scope **) nenofex->scopes->top - 1;
  assert (nenofex->cur_scope >= (Scope **) nenofex->scopes->elems);

  assert (!nenofex->next_scope);
  if (nenofex->cur_scope - 1 > (Scope **) nenofex->scopes->elems)
    {                           /* typically QBF */
      nenofex->next_scope = nenofex->cur_scope - 1;
      assert (nenofex->cur_scope > (Scope **) nenofex->scopes->elems);
      /* default scope unused */
      (*((Scope **) nenofex->scopes->elems))->is_empty = 1;
      assert (is_empty_scope
              (nenofex, (*((Scope **) nenofex->scopes->elems))));
    }
  else if (nenofex->cur_scope - 1 == (Scope **) nenofex->scopes->elems)
    {                           /* default scope unused */
      (*((Scope **) nenofex->scopes->elems))->is_empty = 1;
      assert (is_empty_scope
              (nenofex, (*((Scope **) nenofex->scopes->elems))));
    }

  /* initialize cur. scope from scratch once at startup */
  init_all_scope_variable_scores (nenofex, *nenofex->cur_scope);
  init_order_priority_queue ((*nenofex->cur_scope)->priority_heap);

  /* NOTE: calling 'is_existential/universal' could be postponed; 
     should clean up vars without occurrences first */
  nenofex->is_existential = is_formula_existential (nenofex);
  nenofex->is_universal = is_formula_universal (nenofex);

  int full = nenofex->options.full_expansion_specified;
  int limit = nenofex->options.num_expansions_specified;

  int size_cutoff_relative_specified =
    nenofex->options.size_cutoff_relative_specified;
  int size_cutoff_absolute_specified =
    nenofex->options.size_cutoff_absolute_specified;
  assert (!size_cutoff_relative_specified || !size_cutoff_absolute_specified);

  int size_cutoff_specified =
    size_cutoff_relative_specified || size_cutoff_absolute_specified;
  unsigned int size_before_expansion, size_after_expansion;
  size_before_expansion = size_after_expansion = 0;
  int size_increase = 0;

  int cost_cutoff_specified = nenofex->options.cost_cutoff_specified;
  int cost_cutoff = nenofex->options.cost_cutoff;

  int optimize = !nenofex->options.no_optimizations_specified;
  optimize = optimize && (!nenofex->options.no_atpg_specified ||
                          !nenofex->options.no_global_flow_specified);

  /* Use either current size increase as universal trigger or measure
     absolute value of nodes in formula. */
  int universal_trigger;
  if (!nenofex->options.univ_trigger_abs)
    universal_trigger = nenofex->options.univ_trigger;
  else
    universal_trigger = nenofex->graph_root->size_subformula +
      (nenofex->graph_root->size_subformula *
       nenofex->options.univ_trigger_delta / 100);

  /* Flag to indicate that expansion phase is aborted prematurely due
     to user-specific limit (except cost-limit, where cutoff occurs
     before next expansion). */
  unsigned int cutoff_occurred = 0;

  nenofex->cur_expansions = 0;
  while (nenofex->result == NENOFEX_RESULT_UNKNOWN && ((full && !limit) || (full && limit && nenofex->cur_expansions < nenofex->options.num_expansions) || (!full && !limit && !nenofex->is_existential && !nenofex->is_universal) ||   /* std. case */
                                                       (!full && limit
                                                        && nenofex->
                                                        cur_expansions <
                                                        nenofex->options.
                                                        num_expansions
                                                        && !nenofex->
                                                        is_existential
                                                        && !nenofex->
                                                        is_universal)))
    {

      if (nenofex->options.show_graph_size_specified)
        {
          fprintf (stderr, "Graph size: %d\n\n",
                   nenofex->graph_root->size_subformula);
        }

#if COMPUTE_MAX_TREE_SIZE
      if (nenofex->graph_root)
        {
          unsigned int cur_size = nenofex->graph_root->size_subformula;
          if (cur_size > nenofex->stats.max_tree_size)
            nenofex->stats.max_tree_size = cur_size;
        }
#endif

#if PRINT_CLAUSE_COUNT
      int clause_count = nnf_to_cnf_tseitin_revised_count_clauses (nenofex);
      fprintf (stderr, "Clause Count = %d\n\n", clause_count);
#endif

#if COMPUTE_GRAPH_STATISTICS
      compute_graph_statistics (nenofex);
#endif

      assert (!nenofex->changed_subformula.lca ||
              !is_literal_node (nenofex->changed_subformula.lca));
      assert (!nenofex->changed_subformula.lca ||
              nenofex->changed_subformula.num_children >= 2);

#ifndef NDEBUG
#if ASSERT_POS_IN_CHANGED_CH_LIST
      if (nenofex->changed_subformula.lca)
        assert_pos_in_changed_ch_list (nenofex);
#endif
#endif

      assert (nenofex->cur_scope);
      assert (nenofex->cur_scope >= (Scope **) nenofex->scopes->elems);
      assert (!nenofex->next_scope ||
              nenofex->next_scope >= (Scope **) nenofex->scopes->elems);
      assert (nenofex->next_scope < (Scope **) nenofex->scopes->elems ||
              nenofex->next_scope);

      assert (!nenofex->atpg_rr_called);
      assert (!nenofex->atpg_rr_reset_changed_subformula);

      if (simplify_eliminate_units (nenofex))
        continue;

      int unates;
      if ((unates = simplify_eliminate_unates (nenofex)))
        {
          if (nenofex->options.show_progress_specified)
            fprintf (stderr, "Found %d unates\n", unates);
          continue;
        }

#ifndef NDEBUG
#if ASSERT_SCOPE_VAR_CNT
      assert_all_scope_variable_counts (nenofex);
#endif
#endif


/*
- NOTE: on CNFs, ATPG/GlobalFlow do rather not succeed after exp. of negative-score-vars?
*/

      if (optimize)
        {
          nenofex->performed_optimizations++;

          if (simplify_by_global_flow_and_atpg (nenofex))
            {
              nenofex->successful_optimizations++;

              if (nenofex->cur_expansions > 0
                  && !nenofex->first_successful_opt)
                nenofex->first_successful_opt = nenofex->cur_expansions;

#ifndef NDEBUG
#if ASSERT_GRAPH_AFTER_ATPG_GLOBAL_FLOW
              assert (!nenofex->cur_expanded_var);
              assert_all_child_occ_lists_integrity (nenofex);
              assert_all_occ_lists_integrity (nenofex);
              assert_all_subformula_sizes (nenofex);
#endif
#endif
              continue;
            }
        }                       /* end: if optimizations enabled */
      else if (1)               /* NOTE: reset 'changed-subgraph' if no opt. performed (?) */
        reset_changed_lca_object (nenofex);

#ifndef NDEBUG
#if ASSERT_ALL_SCOPES_FREE_OF_NO_OCC_VARS
      assert_all_scopes_free_of_no_occ_vars (nenofex);
#endif
#endif

      /* check if formula is exist. / univ. - NOTE: this could be done incrementally */
      if (!full && nenofex->result == NENOFEX_RESULT_UNKNOWN)
        {
          nenofex->is_existential = is_formula_existential (nenofex);
          if (!nenofex->is_existential)
            nenofex->is_universal = is_formula_universal (nenofex);
          else
            nenofex->is_universal = 0;
        }
      else if (!full)
        {
          assert (!nenofex->is_existential);
          assert (!nenofex->is_universal);
        }

      if (!full && (nenofex->is_existential || nenofex->is_universal))
        {                       /* will exit loop immediately */
          nenofex->sat_solver_tautology_mode = nenofex->is_universal;
          continue;
        }
      /* end: check if formula is existential */

      /* NOTE: if cutoff occurs after expansion due to ANY
	 user-specific limit (except cost-limit, which takes effect
	 before an expansion), then we must not exit loop immediately
	 but enter another iteration and proceed until here since
	 simplifications are performed to properly set up counters
	 etc. */
      if (cutoff_occurred)
	break;

      if (nenofex->graph_root)
        size_before_expansion = nenofex->graph_root->size_subformula;
      else
        size_before_expansion = 0;

      int non_inner_univ_exp = nenofex->consider_univ_exp;
      var = pick_variable_for_expansion (nenofex);

#ifndef NDEBUG
#if  ASSERT_ALL_SCOPES_PRIORITY_QUEUE_HEAP_CONDITION
      assert_all_scopes_priority_queue_heap_condition (nenofex);
#endif
#endif

      assert (!nenofex->cur_scope ||
              *nenofex->cur_scope ==
              find_innermost_non_empty_scope (nenofex));
      assert (var);

      /* check if cost-cutoff specified */
      if (cost_cutoff_specified)
        {
          if (var->exp_costs.score > cost_cutoff)
            {
              if (!nenofex->options.print_short_answer_specified)
                fprintf (stderr,
                         "\n\tCOST CUTOFF: cutoff = %d, current cost = %d\n\n",
                         cost_cutoff, var->exp_costs.score);
              break;
            }
        }                       /* end: cost_cutoff specified */

      if (nenofex->options.show_progress_specified)
        {
          if ((*nenofex->cur_scope)->nesting != DEFAULT_SCOPE_NESTING)
            {
              fprintf (stderr, "Expansion (%c): var %d, cost %d from "
                       "scope %d (%d remaining, %d in next scope)\n\n",
                       is_existential_scope (var->scope) ? 'E' : 'A',
                       var->id, var->exp_costs.score, var->scope->nesting,
                       nenofex->num_cur_remaining_scope_vars,
                       nenofex->next_scope ? (*nenofex->next_scope)->
                       remaining_var_cnt : 0);
            }
          else
            {
              fprintf (stderr,
                       "Expanding min. cost var (%c): %d with cost %d "
                       "(with %d variables remaining)\n\n",
                       is_existential_scope (var->scope) ? 'E' : 'A', var->id,
                       var->exp_costs.score,
                       nenofex->num_cur_remaining_scope_vars);
            }
        }

      mark_affected_scope_variables_for_cost_update (nenofex,
                                                     var->exp_costs.
                                                     lca_object.lca);

#if PRINT_LIT_STATS_BEFORE_EXP
      if (var->scope->nesting == (*nenofex->cur_scope)->nesting)
        print_lit_stats_before_exp (nenofex, var);
#endif

      if (is_existential_scope (var->scope))
        {
          assert (!non_inner_univ_exp);
          expand_existential_variable (nenofex, var);
        }
      else
        {
          expand_universal_variable (nenofex, var);
          if (non_inner_univ_exp && nenofex->options.univ_trigger_abs)
            {
              int new_trigger = nenofex->graph_root->size_subformula +
                (nenofex->graph_root->size_subformula *
                 nenofex->options.univ_trigger_delta / 100);
              if (new_trigger > universal_trigger)
                {
                  universal_trigger = new_trigger;
                  if (nenofex->options.show_progress_specified)
                    fprintf (stderr, "New univ-trigger-abs: %d\n",
                             universal_trigger);
                }
            }
        }

      nenofex->cur_expansions++;
      if (nenofex->graph_root)
        size_after_expansion = nenofex->graph_root->size_subformula;
      else
        size_after_expansion = 0;
      size_increase = size_after_expansion - size_before_expansion;

      if (nenofex->next_scope &&
          is_existential_scope (var->scope) &&
          ((!nenofex->options.univ_trigger_abs
            && (size_increase > universal_trigger))
           ||
           ((nenofex->options.univ_trigger_abs
             && (nenofex->graph_root
                 && nenofex->graph_root->size_subformula >
                 universal_trigger))))
          && is_universal_scope (*nenofex->next_scope)
          && is_existential_scope (*nenofex->cur_scope))
        {
          nenofex->consider_univ_exp = 1;

          if (!nenofex->options.univ_trigger_abs)
            universal_trigger += nenofex->options.univ_trigger_delta;
          else
            {
#if 0
              universal_trigger = nenofex->graph_root->size_subformula +
                (nenofex->graph_root->size_subformula *
                 nenofex->options.univ_trigger_delta / 100);
              if (nenofex->options.show_progress_specified)
                fprintf (stderr, "New univ-trigger-abs: %d\n",
                         universal_trigger);
#endif
            }
        }
      else
        {
          assert (nenofex->consider_univ_exp == 0);
        }

      /* check if size-cutoff occurred */
      if (size_cutoff_specified)
        {
          if (size_cutoff_relative_specified)
            {
              if (size_after_expansion >
                  (size_before_expansion *
                   (1 + nenofex->options.size_cutoff)))
                {
                  if (!nenofex->options.print_short_answer_specified)
                    fprintf (stderr,
                             "\n\tSIZE CUTOFF: cutoff = %f, before = %d, after = %d\n\n",
                             nenofex->options.size_cutoff,
                             size_before_expansion, size_after_expansion);
		  assert (!cutoff_occurred);
                  cutoff_occurred = 1;
                }
            }
          else                  /* absolute cutoff */
            {
              if (size_after_expansion >
                  (size_before_expansion + nenofex->options.size_cutoff))
                {
                  if (!nenofex->options.print_short_answer_specified)
                    fprintf (stderr,
                             "\n\tSIZE CUTOFF: cutoff = %f, size before = %d, size after = %d\n\n",
                             nenofex->options.size_cutoff,
                             size_before_expansion, size_after_expansion);
		  assert (!cutoff_occurred);
		  cutoff_occurred = 1;
                }
            }
        }                       /* end: size_cutoff specified */

      /* Check for absolute cutoff limit */
      if (nenofex->options.abs_graph_size_cutoff > 0)
        {
          if (nenofex->graph_root && 
              nenofex->graph_root->size_subformula > 
              nenofex->options.abs_graph_size_cutoff * nenofex->init_graph_size)
            {
              if (!nenofex->options.print_short_answer_specified)
                fprintf (stderr,
                         "\n\tGRAPH SIZE CUTOFF: cutoff = %f, init size = %d, cur size = %d\n\n",
                         nenofex->options.abs_graph_size_cutoff,
                         nenofex->init_graph_size, nenofex->graph_root->size_subformula);
	      assert (!cutoff_occurred);
	      cutoff_occurred = 1;
            }
        }

#ifndef NDEBUG
#if ASSERT_AFTER_EXP_ALL_NON_INNERMOST_SCOPE_VARS_UNINIT
      assert_all_non_innermost_scope_vars_uninitialized (nenofex,
                                                         nenofex->cur_scope);
#endif
#endif

    }                           /* end: elimination-while */

  nenofex->expansion_phase_end_time = time_stamp ();
}


static void
sat_solving_phase (Nenofex * nenofex)
{
  int dump = nenofex->options.dump_cnf_specified;
  int forward = !nenofex->options.no_sat_solving_specified;
  assert (dump || forward);

  if (nenofex->result == NENOFEX_RESULT_UNKNOWN
      && !nenofex->sat_solver_tautology_mode)
    {
      assert (is_formula_existential (nenofex));

      if (forward)
        {
          sat_solver_init (nenofex);
          if (nenofex->options.verbose_sat_solving_specified)
            sat_solver_verbosity_mode (nenofex);
          nnf_to_cnf_forward (nenofex);
        }

      if (dump)                 /* note: cnf is generated from scratch if this option is toggled */
        nnf_to_cnf_dump (nenofex, stdout);

      if (forward)
        {
          int sat_res = sat_solver_sat (nenofex);

          if (sat_res == SAT_SOLVER_RESULT_UNKNOWN)
            {
              if (!nenofex->options.print_short_answer_specified)
                fprintf (stderr,
                         "\n\tSAT solver result unknown due to decision limit %u\n\n",
                         nenofex->options.sat_solver_dec_limit);
            }
          nenofex->stats.sat_solver_decisions = picosat_decisions (nenofex->picosat);

          nenofex->result = sat_res;

          if (nenofex->options.print_assignment_specified &&
              nenofex->result == NENOFEX_RESULT_SAT)
            {
              get_var_assignments_from_sat_solver (nenofex);
              generate_qdimacs_output (nenofex, stdout);
            }

          sat_solver_reset (nenofex);
        }
    }                           /* end: propositional formula */


  if (nenofex->result == NENOFEX_RESULT_UNKNOWN
      && nenofex->sat_solver_tautology_mode)
    {
      assert (is_formula_universal (nenofex));

      if (forward)
        {
          sat_solver_init (nenofex);
          if (nenofex->options.verbose_sat_solving_specified)
            sat_solver_verbosity_mode (nenofex);
          nnf_to_cnf_forward (nenofex);
        }

      if (dump)                 /* note: cnf is generated from scratch if this option is toggled */
        nnf_to_cnf_dump (nenofex, stdout);

      if (forward)
        {
          int sat_res = sat_solver_sat (nenofex);

          if (sat_res == SAT_SOLVER_RESULT_UNKNOWN)
            fprintf (stderr,
                     "\n\tSAT solver result unknown due to decision limit %u\n\n",
                     nenofex->options.sat_solver_dec_limit);
          nenofex->stats.sat_solver_decisions = picosat_decisions (nenofex->picosat);

          /* Handle unknown SAT solver result, may happen due to decision limit. */
          if (sat_res != SAT_SOLVER_RESULT_UNKNOWN)
            {
              nenofex->result = sat_res == SAT_SOLVER_RESULT_SATISFIABLE ?
                NENOFEX_RESULT_UNSAT : NENOFEX_RESULT_SAT;
            }

          if (nenofex->options.print_assignment_specified &&
              nenofex->result == NENOFEX_RESULT_UNSAT)
            {                   /* implies sat-solver returned SAT */
              get_var_assignments_from_sat_solver (nenofex);
              generate_qdimacs_output (nenofex, stdout);
            }

          sat_solver_reset (nenofex);
        }
    }                           /* end: universal formula */
}


static int
count_scope_variables (Nenofex * nenofex, Scope * scope)
{
  int result = 0;

  void **v_var, **var_end;
  var_end = scope->vars->top;
  for (v_var = scope->vars->elems; v_var < var_end; v_var++)
    {
      Var *var = *v_var;
      if (variable_has_occs (var))
        result++;
    }

  return result;
}


static int
count_variables (Nenofex * nenofex, const int count_existential)
{
  int result = 0;

  void **v_scope, **scope_end;
  scope_end = nenofex->scopes->top;
  for (v_scope = nenofex->scopes->elems; v_scope < scope_end; v_scope++)
    {
      Scope *scope = *v_scope;
      if (count_existential && is_existential_scope (scope))
        result += count_scope_variables (nenofex, scope);
      else if (!count_existential && is_universal_scope (scope))
        result += count_scope_variables (nenofex, scope);
    }

  return result;
}


static void
print_statistics_at_start (Nenofex * nenofex)
{
  int graph_size =
    nenofex->graph_root ? nenofex->graph_root->size_subformula : 0;
  int num_clauses_specified = nenofex->num_orig_clauses;
  int num_vars_specified = nenofex->num_orig_vars;
  int num_exist_vars = count_variables (nenofex, 1);
  int num_univ_vars = count_variables (nenofex, 0);

  fprintf (stderr, "\nEntering expansion phase:\n");
  fprintf (stderr, "  tree size: %d\n", graph_size);
  fprintf (stderr, "  specified number of variables: %d (E: %d, A: %d)\n",
           num_vars_specified, num_exist_vars, num_univ_vars);
  fprintf (stderr, "  specified number of clauses: %d (current: %d)\n",
           num_clauses_specified,
           nnf_to_cnf_tseitin_revised_count_clauses (nenofex));
}


static void
print_statistics_after_expansion (Nenofex * nenofex)
{
  int graph_size =
    nenofex->graph_root ? nenofex->graph_root->size_subformula : 0;
  int num_exist_vars = count_variables (nenofex, 1);
  int num_univ_vars = count_variables (nenofex, 0);

  fprintf (stderr, "\nAfter expansion phase:\n");
  fprintf (stderr, "  tree size: %d\n", graph_size);
#if COMPUTE_MAX_TREE_SIZE
  fprintf (stderr, "  max. tree size: %d\n", nenofex->stats.max_tree_size);
#endif
#if COMPUTE_NUM_UNITS
  fprintf (stderr, "  units: %d\n", nenofex->stats.num_units);
#endif
#if COMPUTE_NUM_UNATES
  fprintf (stderr, "  unates: %d\n", nenofex->stats.num_unates);
#endif
  fprintf (stderr, "  expansions: %d\n", nenofex->cur_expansions);
#if COMPUTE_CASES_IN_EXPANSIONS
  fprintf (stderr, "    case [E,OR,=]: %d\n",
           nenofex->stats.num_exp_case_E_OR_ALL);
  fprintf (stderr, "    case [E,OR,<]: %d\n",
           nenofex->stats.num_exp_case_E_OR_SUBSET);
  fprintf (stderr, "    case [E,AND,=]: %d\n",
           nenofex->stats.num_exp_case_E_AND_ALL);
  fprintf (stderr, "    case [E,AND,<]: %d\n",
           nenofex->stats.num_exp_case_E_AND_SUBSET);
  fprintf (stderr, "    case [A,AND,=]: %d\n",
           nenofex->stats.num_exp_case_A_AND_ALL);
  fprintf (stderr, "    case [A,AND,<]: %d\n",
           nenofex->stats.num_exp_case_A_AND_SUBSET);
  fprintf (stderr, "    case [A,OR,=]: %d\n",
           nenofex->stats.num_exp_case_A_OR_ALL);
  fprintf (stderr, "    case [A,OR,<]: %d\n",
           nenofex->stats.num_exp_case_A_OR_SUBSET);
#endif
#if COMPUTE_NUM_NON_INC_EXPANSIONS_IN_SCORES
  fprintf (stderr, "  possible non-inc. expansions: %d\n",
           nenofex->stats.num_non_inc_expansions_in_scores);
#endif
#if COMPUTE_NUM_NON_INC_EXPANSIONS
  fprintf (stderr, "  actual non-inc. expansions: %d\n",
           nenofex->stats.num_non_inc_expansions);
#endif
  fprintf (stderr, "  expansion time: %.2fs\n",
           nenofex->expansion_phase_end_time - nenofex->start_time);
#if COMPUTE_AVERAGE_UPDATE_MARKED_RATIOS
  if (nenofex->cur_expansions)
    {
      fprintf (stderr, "  avg. ratio lca-marked / remaining scope vars: %f\n",
               nenofex->stats.sum_ratio_lca_marked_in_scope_vars /
               nenofex->cur_expansions);
      fprintf (stderr, "  avg. ratio inc-marked / remaining scope vars: %f\n",
               nenofex->stats.sum_ratio_inc_marked_in_scope_vars /
               nenofex->cur_expansions);
      fprintf (stderr, "  avg. ratio dec-marked / remaining scope vars: %f\n",
               nenofex->stats.sum_ratio_dec_marked_in_scope_vars /
               nenofex->cur_expansions);
      double avg_remaining =
        (double) nenofex->stats.sum_remaining / nenofex->cur_expansions;
      fprintf (stderr, "  avg. remaining scope vars %f\n", avg_remaining);
      fprintf (stderr, "  avg. lca-marked in remaining scope vars: %f\n",
               (double) nenofex->stats.sum_lca_marked /
               nenofex->cur_expansions);
      fprintf (stderr, "  avg. inc-marked in remaining scope vars: %f\n",
               (double) nenofex->stats.sum_inc_marked /
               nenofex->cur_expansions);
      fprintf (stderr, "  avg. dec-marked in remaining scope vars: %f\n",
               (double) nenofex->stats.sum_dec_marked /
               nenofex->cur_expansions);
    }
#endif
#if COMPUTE_LCA_PARENT_VISITS
  if (nenofex->stats.num_total_lca_algo_calls)
    fprintf (stderr,
             "  avg. parent visits in LCA computation: %f (total %d calls)\n",
             (double) nenofex->stats.num_total_lca_parent_visits /
             nenofex->stats.num_total_lca_algo_calls,
             nenofex->stats.num_total_lca_algo_calls);
#endif
  fprintf (stderr, "  optimizations called: %d\n",
           nenofex->performed_optimizations);
  fprintf (stderr, "  optimizations succeeded: %d\n",
           nenofex->successful_optimizations);
  fprintf (stderr, "  first successful optimizations after %d expansions\n",
           nenofex->first_successful_opt);
  if (nenofex->options.post_expansion_flattening_specified)
    fprintf (stderr, "  post-expansion flattening applied: %d\n",
             nenofex->cnt_post_expansion_flattenings);
  fprintf (stderr, "  remaining orig. variables: %d (E: %d, A: %d)\n",
           num_exist_vars + num_univ_vars, num_exist_vars, num_univ_vars);
#if COMPUTE_NUM_TOTAL_CREATED_NODES
  fprintf (stderr, "  total created nodes: %d\n",
           nenofex->stats.num_total_created_nodes);
#endif

#if COMPUTE_NUM_DELETED_NODES
  fprintf (stderr,
           "  total deleted nodes: %d with %.3f%% (%d) in optimizations\n",
           nenofex->stats.total_deleted_nodes,
           nenofex->stats.deleted_nodes_by_global_flow_redundancy /
           (float) nenofex->stats.total_deleted_nodes * 100,
           nenofex->stats.deleted_nodes_by_global_flow_redundancy);
#endif
}

static void
post_formula_addition_simplified (Nenofex *nenofex)
{
  /* Must prevent multiple calls in parse function and then in solve function. */
  if (nenofex->post_formula_addition_simplified)
    return;
  nenofex->post_formula_addition_simplified = 1;

  if (nenofex->graph_root->num_children == 1)
    {                           /* only one clause parsed -> becomes new graph root */
      assert (nenofex->graph_root->child_list.first);
      assert (nenofex->graph_root->child_list.first ==
              nenofex->graph_root->child_list.last);

      Node *clause = nenofex->graph_root->child_list.first;
      unlink_node (nenofex, clause);
      delete_node (nenofex, nenofex->graph_root);
      nenofex->graph_root = clause;

      clause->level = 0;

      if (!is_literal_node (clause))
        {
          Node *child;
          for (child = clause->child_list.first; child;
               child = child->level_link.next)
            child->level = 1;
        }

      nenofex->first_added_clause = nenofex->second_added_clause = 0; /* need not simplify afterwards */
    }                           /* end: root had only one clause */

  /* simplify first two clauses */
  assert (is_literal_node (nenofex->graph_root)
          || nenofex->graph_root->num_children >= 2);

  if (nenofex->first_added_clause && !is_literal_node (nenofex->first_added_clause))  /* if is not unit */
    {
      simplify_one_level (nenofex, nenofex->first_added_clause);
      if (nenofex->graph_root && is_or_node (nenofex->graph_root))      /* only 1 non-unit left */
        simplify_one_level (nenofex, nenofex->graph_root);
      else if (nenofex->graph_root && !is_literal_node (nenofex->second_added_clause)) /* if not unit */
        simplify_one_level (nenofex, nenofex->second_added_clause);
    }
  else if (nenofex->first_added_clause)        /* first is unit, check second */
    {
      if (nenofex->second_added_clause && !is_literal_node (nenofex->second_added_clause))    /* if not unit */
        simplify_one_level (nenofex, nenofex->second_added_clause);
    }

  /* NOTE: unit elimination is performed -> actually need no 1-l-simp */
  if (nenofex->graph_root && !is_literal_node (nenofex->graph_root))
    simplify_one_level (nenofex, nenofex->graph_root);
}

static void
post_formula_addition_cleanup (Nenofex *nenofex)
{
  if (nenofex->vars)
    {
      mem_free (nenofex->mm, nenofex->vars, (nenofex->num_orig_vars + 1) * sizeof (Var *));
      nenofex->vars = (Var **) 0;
    }
}

/* --------- START: API FUNCTIONS --------- */

Nenofex *
nenofex_create ()
{
  MemManager *mm = memmanager_create ();
  size_t num_bytes = sizeof (Nenofex);
  Nenofex *result = mem_malloc (mm, num_bytes);
  assert (result);
  memset (result, 0, num_bytes);

  result->mm = mm;

  result->start_time = time_stamp ();

  result->scopes = create_stack (mm, DEFAULT_STACK_SIZE);
  result->unates = create_stack (mm, DEFAULT_STACK_SIZE);
  result->depending_vars = create_stack (mm, DEFAULT_STACK_SIZE);
  result->vars_marked_for_update = create_stack (mm, DEFAULT_STACK_SIZE);
  result->atpg_rr = create_atpg_redundancy_remover (mm);

  init_lca_object (result, &(result->changed_subformula));

  /* default settings */
  set_default_cmd_line_options (result);

  add_default_scope (result);

#ifndef NDEBUG
  assert_solver_options (result);
#endif

  return result;
}

void
nenofex_delete (Nenofex *nenofex)
{
  assert (!nenofex->vars);
  MemManager *mm = nenofex->mm;
  free_graph (nenofex);

  free_lca_children (nenofex, &(nenofex->changed_subformula));

  Scope *scope;
  while ((scope = pop_stack (nenofex->scopes)))
    {
      Var *var;
      while ((var = pop_stack (scope->vars)))
        {
          delete_stack (mm, var->pos_in_lca_child_list_occs);
          free_lca_children (nenofex, &(var->exp_costs.lca_object));
          assert (!var->subformula_pos_occs);
          assert (!var->subformula_neg_occs);
          mem_free (mm, var, sizeof (Var));
        }
      delete_scope (nenofex, scope);
    }
  delete_stack (mm, nenofex->scopes);

  delete_stack (mm, nenofex->unates);
  delete_stack (mm, nenofex->vars_marked_for_update);
  delete_stack (mm, nenofex->depending_vars);

  free_atpg_redundancy_remover (nenofex->atpg_rr);
  mem_free (mm, nenofex, sizeof (Nenofex));
  memmanager_delete (mm);
}


NenofexResult 
nenofex_solve (Nenofex *nenofex)
{
  if (nenofex->solve_called)
    {
      fprintf (stderr, "Must not call 'nenofex_solve' more than once!\n");
      exit (1);
    }
  nenofex->solve_called = 1;

#if 0
  /* It should not matter if fewer clauses are added than were declared before. */
  if (!nenofex->empty_clause_added &&
      nenofex->num_added_clauses != nenofex->num_orig_clauses)
    {
      fprintf (stderr, "Numbers of declared and added clauses do not match!\n");
      exit (1);
    }
#endif

  /* Must cleanup regardless of whether added formula is trivial or not. */
  post_formula_addition_cleanup (nenofex);

  /* Handle trivially unsatisfiable formula in library use. */
  if (nenofex->empty_clause_added)
    {
      assert (nenofex->num_added_clauses > 0);
      if (nenofex->result == NENOFEX_RESULT_UNKNOWN)
        nenofex->result = NENOFEX_RESULT_UNSAT;
      else
        assert (nenofex->result == NENOFEX_RESULT_UNSAT);
      goto TRIVIAL_FORMULA;
    }

  /* Handle trivially satisfiable formula in library use. */
  if (nenofex->num_added_clauses == 0)
    {
      if (nenofex->result == NENOFEX_RESULT_UNKNOWN)
        nenofex->result = NENOFEX_RESULT_SAT;
      else
        assert (nenofex->result == NENOFEX_RESULT_SAT);
      goto TRIVIAL_FORMULA;
    }

  /* Simplify added formula to set up invariants. */
  post_formula_addition_simplified (nenofex);

  if (!nenofex->options.print_short_answer_specified)
    print_statistics_at_start (nenofex);

  if (nenofex->result != NENOFEX_RESULT_UNKNOWN)
    {
      assert (!nenofex->graph_root);
      goto TRIVIAL_FORMULA;
    }

  expansion_phase (nenofex);

  if (!nenofex->options.print_short_answer_specified)
    print_statistics_after_expansion (nenofex);

  nenofex->is_existential = is_formula_existential (nenofex);
  nenofex->is_universal = is_formula_universal (nenofex);

  if (nenofex->result == NENOFEX_RESULT_UNKNOWN &&
      (nenofex->is_existential || nenofex->is_universal) &&
      (!nenofex->options.no_sat_solving_specified
       || nenofex->options.dump_cnf_specified))
    {
      sat_solving_phase (nenofex);
    }
  else if (nenofex->result == NENOFEX_RESULT_UNKNOWN
           && nenofex->options.dump_cnf_specified)
    {
      /* Dump quantified NNF. */
      quantified_nnf_to_cnf_dump (nenofex, stdout);
    }

 TRIVIAL_FORMULA:

  if (!nenofex->options.print_short_answer_specified)
    {
      fprintf (stderr, "\nfinished after %d expansions\n",
               nenofex->cur_expansions);
    }

  nenofex->end_time = time_stamp ();

  double total_time = nenofex->end_time - nenofex->start_time;
  double expansion_time =
    nenofex->expansion_phase_end_time - nenofex->start_time;

  if (expansion_time < 0)
    expansion_time = 0;

  if (!nenofex->options.print_short_answer_specified)
    {
    fprintf (stderr, "time:\t%.2fs with %.2fs in expansions\n",
             total_time, expansion_time);
    fprintf (stderr, "SAT solver decisions: %llu\n", nenofex->stats.sat_solver_decisions);
    }

  return nenofex->result;
}

/*
- parse and configure by configure-string
*/
void
nenofex_configure (Nenofex * nenofex, char *opt_str)
{
  if (nenofex->solve_called)
    {
      fprintf (stderr, "Must not call 'nenofex_configure' after solving!\n");
      exit (1);
    }

  if (!strncmp (opt_str, "-n=", strlen ("-n=")))
    {
      nenofex->options.num_expansions_specified = 1;
      opt_str += strlen ("-n=");

      if (is_unsigned_string (opt_str))
	{
	  nenofex->options.num_expansions = atoi (opt_str);
	  if (nenofex->options.num_expansions == 0)
	    {
	      fprintf (stderr, "Expecting value > 0 after '-n='\n\n");
	      exit (1);
	    }
	}
      else
	{
	  fprintf (stderr,
		   "Expecting non-zero positive integer after '-n='\n\n");
	  exit (1);
	}
    }
  else if (!strncmp (opt_str, "--abs-graph-size-cutoff=", strlen ("--abs-graph-size-cutoff=")))
    {
      opt_str += strlen ("--abs-graph-size-cutoff=");
      if (strlen (opt_str) == 0)
	{
	  fprintf (stderr, "Expecting value after '--abs-graph-size-cutoff='\n\n");
	  exit (1);
	}
      nenofex->options.abs_graph_size_cutoff = strtof (opt_str, 0);
      if (nenofex->options.abs_graph_size_cutoff < 0)
        {
	  fprintf (stderr,
		   "Expecting positive value after '--abs-graph-size-cutoff='\n\n");
	  exit (1);
        }
    }
  else if (!strncmp (opt_str, "--size-cutoff=", strlen ("--size-cutoff=")))
    {
      opt_str += strlen ("--size-cutoff=");

      if (strlen (opt_str) == 0)
	{
	  fprintf (stderr, "Expecting value after '--size-cutoff='\n\n");
	  exit (1);
	}

      double size_cutoff = atof (opt_str);

      double integer = 0;
      double fractional = modf (size_cutoff, &integer);

      if (fractional)
	{                   /* relative size cutoff */
	  if ((size_cutoff <= -1.0F) || (size_cutoff >= 1.0F))
	    {
	      fprintf (stderr,
		       "Expecting '-1.0 < size_cutoff < 1.0' or an integer\n\n");
	      exit (1);
	    }

	  nenofex->options.size_cutoff_relative_specified = 1;
	}
      else                  /* absolute size cutoff */
	{
	  nenofex->options.size_cutoff_absolute_specified = 1;
	}

      nenofex->options.size_cutoff = size_cutoff;
    }
  else if (!strncmp (opt_str, "--cost-cutoff=", strlen ("--cost-cutoff=")))
    {
      opt_str += strlen ("--cost-cutoff=");

      if (strlen (opt_str) == 0)
	{
	  fprintf (stderr, "Expecting value after '--cost-cutoff='\n\n");
	  exit (1);
	}

      nenofex->options.cost_cutoff_specified = 1;
      nenofex->options.cost_cutoff = atoi (opt_str);
    }
  else if (!strncmp
	   (opt_str, "--propagation-limit=",
	    strlen ("--propagation-limit=")))
    {
      opt_str += strlen ("--propagation-limit=");

      if (strlen (opt_str) == 0)
	{
	  fprintf (stderr,
		   "Expecting value after '--propagation-limit='\n\n");
	  exit (1);
	}

      nenofex->options.propagation_limit_specified = 1;

      if (is_unsigned_string (opt_str))
	{
	  nenofex->options.propagation_limit = atoi (opt_str);
	}
      else
	{
	  fprintf (stderr,
		   "Expecting positive integer after '--propagation-limit='\n\n");
	  exit (1);
	}
    }
  else if (!strncmp (opt_str, "--univ-trigger=", strlen ("--univ-trigger=")))
    {
      opt_str += strlen ("--univ-trigger=");

      if (strlen (opt_str) == 0)
	{
	  fprintf (stderr,
		   "Expecting value or 'abs' after '--univ-trigger='\n\n");
	  exit (1);
	}

      if (is_unsigned_string (opt_str))
	{
	  nenofex->options.univ_trigger_abs = 0;
	  nenofex->options.univ_trigger = atoi (opt_str);
	}
      else
	{
	  if (!strcmp (opt_str, "abs"))
	    nenofex->options.univ_trigger_abs = 1;
	  else
	    {
	      fprintf (stderr,
		       "Expecting positive integer or 'abs' after '--univ-trigger='\n\n");
	      exit (1);
	    }
	}
    }
  else if (!strncmp (opt_str, "--univ-delta=", strlen ("--univ-delta=")))
    {
      opt_str += strlen ("--univ-delta=");

      if (strlen (opt_str) == 0)
	{
	  fprintf (stderr, "Expecting value after '--univ-delta='\n\n");
	  exit (1);
	}

      if (is_unsigned_string (opt_str))
	{
	  nenofex->options.univ_trigger_delta = atoi (opt_str);
	}
      else
	{
	  fprintf (stderr,
		   "Expecting positive integer after '--univ-delta='\n\n");
	  exit (1);
	}
    }
  else if (!strncmp
	   (opt_str, "--opt-subgraph-limit=",
	    strlen ("--opt-subgraph-limit=")))
    {
      opt_str += strlen ("--opt-subgraph-limit=");

      if (strlen (opt_str) == 0)
	{
	  fprintf (stderr,
		   "Expecting value after '--opt-subgraph-limit='\n\n");
	  exit (1);
	}

      if (is_unsigned_string (opt_str))
	{
	  nenofex->options.opt_subgraph_limit = atoi (opt_str);
	  if (nenofex->options.opt_subgraph_limit == 0)
	    {
	      fprintf (stderr,
		       "Expecting value > 0 after '--opt-subgraph-limit='\n\n");
	      exit (1);
	    }
	}
      else
	{
	  fprintf (stderr,
		   "Expecting non-zero positive integer after '--opt-subgraph-limit='\n\n");
	  exit (1);
	}

      nenofex->options.opt_subgraph_limit_specified = 1;
    }
  else if (!strncmp
	   (opt_str, "--sat-solver-dec-limit=",
	    strlen ("--sat-solver-dec-limit=")))
    {
      opt_str += strlen ("--sat-solver-dec-limit=");
      if (strlen (opt_str) == 0)
	{
	  fprintf (stderr,
		   "Expecting value after '--sat-solver-dec-limit='\n\n");
	  exit (1);
	}
      if (is_unsigned_string (opt_str))
        nenofex->options.sat_solver_dec_limit = atoi (opt_str);
      else
	{
	  fprintf (stderr,
		   "Expecting positive integer after '--sat-solver-dec-limit='\n\n");
	  exit (1);
	}
    }
  else if (!strcmp (opt_str, "--verbose-sat-solving"))
    {
      nenofex->options.verbose_sat_solving_specified = 1;
    }
  else if (!strcmp (opt_str, "-v"))
    {
      nenofex->options.print_short_answer_specified = 0;
    }
  else if (!strcmp (opt_str, "--no-optimizations"))
    {
      nenofex->options.no_optimizations_specified = 1;
    }
  else if (!strcmp (opt_str, "--post-expansion-flattening"))
    {
      nenofex->options.post_expansion_flattening_specified = 1;
    }
  else if (!strcmp (opt_str, "--no-atpg"))
    {
      nenofex->options.no_atpg_specified = 1;
    }
  else if (!strcmp (opt_str, "--no-global-flow"))
    {
      nenofex->options.no_global_flow_specified = 1;
    }
  else if (!strcmp (opt_str, "--full-expansion"))
    {
      nenofex->options.full_expansion_specified = 1;
    }
  else if (!strcmp (opt_str, "--dump-cnf"))
    {
      nenofex->options.dump_cnf_specified = 1;
    }
  else if (!strcmp (opt_str, "--no-sat-solving"))
    {
      nenofex->options.no_sat_solving_specified = 1;
    }
  else if (!strcmp (opt_str, "--show-progress"))
    {
      nenofex->options.show_progress_specified = 1;
    }
  else if (!strcmp (opt_str, "--show-opt-info"))
    {
      nenofex->options.show_opt_info_specified = 1;
    }
  else if (!strcmp (opt_str, "--show-graph-size"))
    {
      nenofex->options.show_graph_size_specified = 1;
    }
#if 0                           /* does not yet work */
  else if (!strcmp (opt_str, "--print-assignment"))
    {
      nenofex->options.print_assignment_specified = 1;
    }
#endif
  else if (!strncmp
	   (opt_str, "--cnf-generator=", strlen ("--cnf-generator=")))
    {
      opt_str += strlen ("--cnf-generator=");
      if (!strcmp (opt_str, "tseitin"))
	{
	  nenofex->options.cnf_generator_tseitin_specified = 1;
	  nenofex->options.cnf_generator_tseitin_revised_specified = 0;
	}
      else if (!strcmp (opt_str, "tseitin_revised"))
	{
	  nenofex->options.cnf_generator_tseitin_revised_specified = 1;
	  nenofex->options.cnf_generator_tseitin_specified = 0;
	}
      else
	{
	  fprintf (stderr, "Unknown option %s\n", opt_str);
	  exit (1);
	}
    }
  else if (!strncmp (opt_str, "-", 1) || !strncmp (opt_str, "--", 2))
    {
      fprintf (stderr, "Unknown option %s\n", opt_str);
      exit (1);
    }
  else
    {
      fprintf (stderr, "Unknown option %s\n", opt_str);
      exit (1);
    }
#ifndef NDEBUG
  assert_solver_options (nenofex);
#endif
}

/*
- TODO: refinements
- NOTE: root need not be simplified by one-level-simplification 
- returns result (i.e. nonzero) iff the parsed formula is trivial
*/
NenofexResult 
nenofex_parse (Nenofex * nenofex, FILE * input_file)
{
  if (nenofex->solve_called)
    {
      fprintf (stderr, "Must not call 'nenofex_parse' after solving!\n");
      exit (1);
    }

  unsigned int clause_cnt = 0;
  int closed = 1;
  int preamble_found = 0;
  NenofexResult result = NENOFEX_RESULT_UNKNOWN;
  ScopeType parsed_scope_type = 0;
  Stack *lit_stack = create_stack (nenofex->mm, DEFAULT_STACK_SIZE);

  char c;
  while ((c = fgetc (input_file)) != EOF)
    {
      assert (nenofex->result == NENOFEX_RESULT_UNKNOWN);

      if (c == 'c')
        {
          while ((c = fgetc (input_file)) != EOF && c != '\n')
            ;
        }
      else if (c == 'p')
        {
          if (preamble_found)
            {
              fprintf (stderr, "Preamble already occurred!\n\n");
              exit (1);
            }

          if ((c = fgetc (input_file)) != ' ' ||
              (c = fgetc (input_file)) != 'c' ||
              (c = fgetc (input_file)) != 'n' ||
              (c = fgetc (input_file)) != 'f' ||
              (c = fgetc (input_file)) != ' ')
            {
              fprintf (stderr, "Malformed preamble!\n\n");
              exit (1);
            }

          char num_vars_str[128] = { '\0' };
          char num_clauses_str[128] = { '\0' };

          fscanf (input_file, "%s", num_vars_str);
          fscanf (input_file, "%s", num_clauses_str);

          if (!is_unsigned_string (num_vars_str)
              || !is_unsigned_string (num_clauses_str))
            {
              fprintf (stderr, "Malformed preamble!\n\n");
              exit (1);
            }

          unsigned int num_vars, num_clauses;
          num_vars = atoi (num_vars_str);
          num_clauses = atoi (num_clauses_str);

          nenofex_set_up_preamble (nenofex, num_vars, num_clauses);

          preamble_found = 1;
        }
      else if (c == '-' || isdigit (c))
        {
          if (!preamble_found)
            {
              fprintf (stderr, "Preamble missing!\n\n");
              exit (1);
            }


          closed = 0;

          ungetc (c, input_file);

          long int val;
          fscanf (input_file, "%ld", &val);

          if (val == 0)
            {
              if (!parsed_scope_type)   /* parsing a clause */
                {
                  clause_cnt++;

                  nenofex_add_orig_clause (nenofex, lit_stack->elems, count_stack (lit_stack));
		  assert (clause_cnt == nenofex->num_added_clauses);

                  if (count_stack (lit_stack) == 0)
                    {           /* empty clause */
                      result = NENOFEX_RESULT_UNSAT;
                      nenofex->result = NENOFEX_RESULT_UNSAT;
                      goto SKIP_SIMPLIFY;
                    }

                  /*clause_closed = 1; */
                }
              else              /* parsing a scope */
                {
                  nenofex_add_orig_scope (nenofex, lit_stack->elems, count_stack (lit_stack), parsed_scope_type);
                  parsed_scope_type = 0;
                }

              closed = 1;
              reset_stack (lit_stack);
            }
          else
            {
              push_stack (nenofex->mm, lit_stack, (void *) val);
            }
        }
      else if (c == 'a')
        {
          parsed_scope_type = SCOPE_TYPE_UNIVERSAL;
          if (!closed)
            {
              fprintf (stderr, "Scope not closed!\n");
              exit (1);
            }
        }
      else if (c == 'e')
        {
          parsed_scope_type = SCOPE_TYPE_EXISTENTIAL;
          if (!closed)
            {
              fprintf (stderr, "Scope not closed!\n");
              exit (1);
            }
        }
      else if (!isspace (c))
        {
          fprintf (stderr, "Parsing: invalid character %c\n", c);
          exit (1);
        }

    }                           /* end: while not end of file */

  assert (nenofex->result == NENOFEX_RESULT_UNKNOWN);

  if (!preamble_found)
    {
      fprintf (stderr, "Preamble missing!\n");
      exit (1);
    }

  if (!closed)
    {
      fprintf (stderr, "Scope or clause not closed!\n");
      exit (1);
    }

  assert (clause_cnt == nenofex->num_added_clauses);
#if 0
  /* It should not matter if fewer clauses are added than were declared before. */
  if (clause_cnt != nenofex->num_orig_clauses)
    {
      fprintf (stderr, "Numbers of clauses do not match!\n");
      exit (1);
    }
#endif

#if 0
  if (count_stack (nenofex->var_stack) != nenofex->num_orig_vars)
    {
      fprintf (stderr,
               "Warning: Number of variables does not match! specified %d, but actually %d\n",
               nenofex->num_orig_vars, count_stack (nenofex->var_stack));
    }
#endif

  if (clause_cnt == 0)
    {                           /* no clause parsed */
      result = NENOFEX_RESULT_SAT;
      nenofex->result = NENOFEX_RESULT_SAT;
      goto SKIP_SIMPLIFY;
    }

  post_formula_addition_simplified (nenofex);

SKIP_SIMPLIFY:

  post_formula_addition_cleanup (nenofex);
  delete_stack (nenofex->mm, lit_stack);

  return result;
}

void
nenofex_set_up_preamble (Nenofex * nenofex, unsigned int num_vars,
                 unsigned int num_clauses)
{
  if (nenofex->solve_called)
    {
      fprintf (stderr, "Must not call 'nenofex_set_up_preamble' after solving!\n");
      exit (1);
    }
  if (nenofex->preamble_set_up)
    {
      fprintf (stderr, "Preamble must be set up exactly once!\n");
      exit (1);
    }
  nenofex->preamble_set_up = 1;

  size_t bytes = (num_vars + 1) * sizeof (Var *);
  nenofex->vars = (Var **) mem_malloc (nenofex->mm, bytes);
  assert (nenofex->vars);
  memset (nenofex->vars, 0, bytes);

  nenofex->num_orig_vars = num_vars;
  nenofex->next_free_node_id = num_vars + 1;
  nenofex->tseitin_next_id = num_vars + 1;
  nenofex->num_orig_clauses = num_clauses;
  set_cnf_root (nenofex);
}

/*
- TODO: refinements
*/
void 
nenofex_add_orig_scope (Nenofex * nenofex, void **lits, unsigned int lit_cnt,
                ScopeType parsed_scope_type)
{
  if (nenofex->solve_called)
    {
      fprintf (stderr, "Must not call 'nenofex_add_orig_scope' after solving!\n");
      exit (1);
    }
  if (!nenofex->preamble_set_up)
    {
      fprintf (stderr, "ERROR: preamble must be set up by 'set_up_preamble' before adding clauses!\n");
      exit (1);
    }
  if (lit_cnt == 0)
    {
      fprintf (stderr, "ERROR: must not add empty scope!\n");
      exit (1);
    }

  Scope *scope = new_scope (nenofex);
  scope->type = parsed_scope_type;
  scope->nesting = count_stack (nenofex->scopes);

  unsigned int i;
  for (i = 0; i < lit_cnt; i++)
    {                           /* TODO: pop instead */
      long int lit = (long int) (lits[i]);

      long unsigned int check_val = (lit < 0 ? -lit : lit);
      if (check_val > nenofex->num_orig_vars)
	{
	  fprintf (stderr, "Literal out of bounds!\n");
	  exit (1);
	}

      if (lit < 0)
        {
          fprintf (stderr, "Variable %ld quantified negatively!\n", lit);
          exit (1);
        }

      if (nenofex->vars[lit])
        {
          fprintf (stderr, "Variable %ld already quantified!\n", lit);
          exit (1);
        }

      init_variable (nenofex, lit, scope);
    }

  push_stack (nenofex->mm, nenofex->scopes, scope);
}

/*
- TODO: refinements
*/
void
nenofex_add_orig_clause (Nenofex * nenofex, void **lits, unsigned int lit_cnt)
{
  if (!nenofex->preamble_set_up)
    {
      fprintf (stderr, "ERROR: preamble must be set up by 'set_up_preamble' before adding clauses!\n");
      exit (1);
    }

  nenofex->num_added_clauses++;

  if (lit_cnt == 0)
    {
      nenofex->empty_clause_added = 1;
      return;
    }

  if (nenofex->num_added_clauses > nenofex->num_orig_clauses)
    {
      fprintf (stderr, "Too many clauses added!\n\n");
      exit (1);
    }

  assert (nenofex->graph_root);
  assert (nenofex->graph_root->size_subformula);

  if (lit_cnt == 1)
    {                           /* adding unit clause */
      unsigned long int abs_lit = (((long int) (lits[0])) < 0 ?
                                   -((long int) (lits[0])) : ((long
                                                                int)
                                                               (lits[0])));
      if (abs_lit > nenofex->num_orig_vars)
	{
	  fprintf (stderr, "Literal out of bounds!\n");
	  exit (1);
	}

      if (!nenofex->vars[abs_lit])
        {
          if (count_stack (nenofex->scopes) != 1 && 
              !nenofex->options.print_short_answer_specified)
            fprintf (stderr,
                     "WARNING: first occ. of var in a clause in formula which is NOT propositional!\n");
          init_variable (nenofex, abs_lit, 0);
        }

      Node *lit_n =
        lit_node (nenofex, ((long int) lits[0]),
                  nenofex->vars[abs_lit]);
      lit_n->size_subformula = 1;
      add_node_to_child_list (nenofex, nenofex->graph_root, lit_n);
      nenofex->graph_root->size_subformula++;
      add_lit_node_to_occurrence_list (nenofex, lit_n);

      add_orig_clause_aux (nenofex, lit_n);
      return;
    }                           /* end: adding unit clause */

  Node *clause = or_node (nenofex);
  add_node_to_child_list (nenofex, nenofex->graph_root, clause);
  clause->size_subformula = 1;

  unsigned int i;
  for (i = 0; i < lit_cnt; i++)
    {
      long int lit = (long int) (lits[i]);
      unsigned long int abs_lit = (lit < 0 ? -lit : lit);

      if (abs_lit > nenofex->num_orig_vars)
	{
	  fprintf (stderr, "Literal out of bounds!\n");
	  exit (1);
	}

      if (!nenofex->vars[abs_lit])
        {
          if (count_stack (nenofex->scopes) != 1)
            fprintf (stderr,
                     "WARNING: first occ. of var in a clause in formula which is NOT propositional!\n");
          init_variable (nenofex, abs_lit, 0);
        }

      Node *lit_n = lit_node (nenofex, lit, nenofex->vars[abs_lit]);
      lit_n->size_subformula = 1;
      add_node_to_child_list (nenofex, clause, lit_n);
      add_lit_node_to_occurrence_list (nenofex, lit_n);
    }                           /* end: for all literals */
  clause->size_subformula += lit_cnt;

  nenofex->graph_root->size_subformula += clause->size_subformula;

  /* keep first two clauses -> simplify after all clauses have been parsed */
  if (nenofex->graph_root->num_children >= 3)
    {
      simplify_one_level (nenofex, clause);
    }

  add_orig_clause_aux (nenofex, clause);
  return;
}

/* --------- END: API FUNCTIONS --------- */
