#Tree Transducer Language Membership





                    # Check if the rule matches the children of the current node
                        # All children matched, apply the rule and return the resulting tree


# Example usage





if __name__ == '__main__':
    class TreeTransducer:
        def __init__(self, rules):
            self.rules = rules
        def apply_transducer(self, input_tree):
            return self.apply_rules(input_tree)
        def apply_rules(self, tree):
            if isinstance(tree, str):
                return tree  # Leaf node, return the label as is
            nonterminal = tree[0]
            children = tree[1:]
            if nonterminal in self.rules:
                for rule in self.rules[nonterminal]:
                    if len(rule) == len(children):
                        new_children = []
                        for i, child in enumerate(children):
                            new_child = self.apply_rules(child)
                            if new_child is None or new_child != rule[i]:
                                break  # Rule doesn't match, move to the next rule
                            new_children.append(new_child)
                        else:
                            return [nonterminal] + new_children
            return None  # No rule matches, return None
    rules = {
        'S': [['A', 'B'], ['C']],
        'A': [['x']],
        'B': [['y']],
        'C': [['z']]
    }
    transducer = TreeTransducer(rules)
    input_tree1 = ['S', ['x'], ['y']]
    input_tree2 = ['S', ['z']]
    result1 = transducer.apply_transducer(input_tree1)
    result2 = transducer.apply_transducer(input_tree2)
    print(f"Input Tree 1 Result: {result1}")
    print(f"Input Tree 2 Result: {result2}")
