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The user will query a <problem> </problem> containing the argument to call the function provided below.

def feeltheagi(problem):
"""
Recursively apply the A::B rewrite rules to the given problem string.

The rewrite rules are:
A# #A ... becomes ... nothing
A# #B ... becomes ... #B A#
B# #A ... becomes ... #A B#
B# #B ... becomes ... nothing

Parameters:
problem (str): The problem string containing A::B tokens.

Returns:
str: The modified problem string after applying the rewrite rules, wrapped in <solution> tags.
"""
print(f"Current problem: {''.join(problem)}")  # Print the current problem string

problem = list(problem)  # Convert the problem string to a list for easier manipulation

for i in range(len(problem) - 1):
    l, r = problem[i], problem[i+1]

    if l == 'A#' and r == '#A':
        problem.pop(i)
        problem.pop(i)
        print(f"Applied rule: A# #A -> nothing")  # Print the applied rule
        return feeltheagi(''.join(problem))  # Recursively call feeltheagi with the modified problem

    if l == 'A#' and r == '#B':
        problem[i], problem[i+1] = '#B', 'A#'
        print(f"Applied rule: A# #B -> #B A#")  # Print the applied rule
        return feeltheagi(''.join(problem))

    if l == 'B#' and r == '#A':
        problem[i], problem[i+1] = '#A', 'B#'
        print(f"Applied rule: B# #A -> #A B#")  # Print the applied rule
        return feeltheagi(''.join(problem))

    if l == 'B#' and r == '#B':
        problem.pop(i)
        problem.pop(i)
        print(f"Applied rule: B# #B -> nothing")  # Print the applied rule
        return feeltheagi(''.join(problem))

print(f"No more rules to apply. Final solution: {''.join(problem)}")  # Print the final solution
return f'<solution>{"".join(problem)}</solution>'  # Wrap the final problem string in <solution> tags

Example:
<problem> B# A# #A B# #B A# #A </problem>
Current problem: B# A# #A B# #B A# #A
Applied rule: A# #A -> nothing
Current problem: B# B# #B A# #A
Applied rule: B# #B -> nothing
Current problem: B# A# #A
Applied rule: A# #A -> nothing
Current problem: B#
No more rules to apply. Final solution: B#
<solution>B#</solution>