#Unification for finitely presented algebras



    # Check if the equations list is empty

    # Choose the first equation from the list

    # Check if the equation is of the form "t = t"

    # Check if the equation is of the form "v = t"

    # Check if the equation is of the form "t = v"

    # Check if the equation is of the form "f(t1, t2, ..., tn) = f(u1, u2, ..., um)"

    # No unification is possible


# Example usage



if __name__ == '__main__':
    def unify_equations(equations):
        equations = list(equations)  # Convert equations to a list
        if len(equations) == 0:
            return True
        equation = equations[0]
        if equation[0] == equation[1]:
            return unify_equations(equations[1:])
        if isinstance(equation[0], str):
            var = equation[0]
            term = equation[1]
            if var in term:
                return False
            new_equations = [(substitute(var, term, eq[0]), substitute(var, term, eq[1])) for eq in equations[1:]]
            return unify_equations(new_equations)
        if isinstance(equation[1], str):
            var = equation[1]
            term = equation[0]
            if var in term:
                return False
            new_equations = [(substitute(var, term, eq[0]), substitute(var, term, eq[1])) for eq in equations[1:]]
            return unify_equations(new_equations)
        if equation[0][0] == equation[1][0]:
            args1 = equation[0][1:]
            args2 = equation[1][1:]
            if len(args1) != len(args2):
                return False
            new_equations = [(args1[i], args2[i]) for i in range(len(args1))]
            return unify_equations(new_equations + equations[1:])
        return False
    def substitute(var, term, expression):
        if expression == var:
            return term
        elif isinstance(expression, list):
            return [substitute(var, term, sub_expr) for sub_expr in expression]
        else:
            return expression
    equations = [(['f', 'x'], 'y'), (['f', 'y'], 'x')]
    result = unify_equations(equations)
    if result:
        print("Equations have a common solution.")
    else:
        print("Equations do not have a common solution.")
