MAYBE

Problem:
 0(0(0(0(0(1(0(1(0(3(2(2(3(3(1(1(3(3(x1)))))))))))))))))) ->
 0(3(0(3(0(2(0(0(1(1(0(1(3(2(0(1(3(3(x1))))))))))))))))))
 0(0(1(1(2(3(0(0(2(3(3(0(0(1(0(2(2(1(x1)))))))))))))))))) ->
 0(1(3(2(0(3(1(2(1(1(0(3(2(0(0(2(0(0(x1))))))))))))))))))
 0(0(1(3(1(0(0(0(2(3(3(1(1(3(0(0(2(2(x1)))))))))))))))))) ->
 0(0(1(3(0(0(3(3(1(2(2(0(3(2(0(0(1(1(x1))))))))))))))))))
 0(0(2(0(0(3(0(2(2(3(3(2(2(2(3(0(2(3(x1)))))))))))))))))) ->
 0(3(2(0(2(2(2(0(0(0(2(3(2(3(2(3(0(3(x1))))))))))))))))))
 0(0(2(1(1(1(0(2(0(1(1(0(3(3(1(3(3(1(x1)))))))))))))))))) ->
 0(3(0(3(1(1(1(1(2(2(3(0(0(1(3(1(1(0(x1))))))))))))))))))
 0(0(2(2(2(2(2(1(2(2(1(1(1(0(2(1(1(1(x1)))))))))))))))))) ->
 0(1(1(2(2(1(1(1(1(2(2(2(0(2(0(2(2(1(x1))))))))))))))))))
 0(0(2(2(3(0(3(3(2(2(0(3(3(2(0(1(3(3(x1)))))))))))))))))) ->
 0(2(0(3(0(3(2(3(0(3(2(3(2(2(0(1(3(3(x1))))))))))))))))))
 0(0(3(3(3(3(1(0(1(0(2(3(1(0(2(0(2(1(x1)))))))))))))))))) ->
 1(0(0(3(1(0(2(3(0(0(1(3(1(3(2(3(2(0(x1))))))))))))))))))
 0(1(1(0(1(2(2(0(0(2(3(3(1(2(1(2(1(1(x1)))))))))))))))))) ->
 0(2(0(1(1(1(1(2(0(3(2(0(2(2(1(3(1(1(x1))))))))))))))))))
 0(1(1(1(0(0(2(2(2(3(0(1(2(0(2(2(3(3(x1)))))))))))))))))) ->
 0(0(0(1(2(1(2(2(3(2(0(1(1(3(2(2(0(3(x1))))))))))))))))))
 0(1(3(0(2(3(1(1(1(0(0(0(0(1(2(2(1(2(x1)))))))))))))))))) ->
 0(0(2(1(2(0(1(2(0(1(2(1(1(1(0(3(0(3(x1))))))))))))))))))
 0(2(0(2(0(3(3(1(2(3(3(2(2(3(1(2(2(3(x1)))))))))))))))))) ->
 2(0(3(2(1(3(3(2(2(2(1(0(3(2(2(0(3(3(x1))))))))))))))))))
 0(2(0(3(3(2(2(1(2(0(0(3(1(3(3(2(3(3(x1)))))))))))))))))) ->
 2(0(3(2(0(1(2(0(2(2(3(0(3(3(3(1(3(3(x1))))))))))))))))))
 0(2(1(0(0(2(0(2(2(3(0(1(0(2(1(1(2(3(x1)))))))))))))))))) ->
 2(0(1(2(2(0(0(2(2(3(0(1(1(0(1(2(0(3(x1))))))))))))))))))
 0(3(3(2(2(3(2(2(2(1(0(3(2(1(0(3(3(2(x1)))))))))))))))))) ->
 0(3(2(3(2(0(3(0(2(2(3(1(1(2(3(2(3(2(x1))))))))))))))))))
 1(0(0(0(0(2(0(0(2(1(0(1(1(3(2(3(2(1(x1)))))))))))))))))) ->
 2(2(0(0(1(3(2(0(1(0(1(3(0(1(0(1(2(0(x1))))))))))))))))))
 1(0(0(0(3(1(2(3(3(3(1(1(0(3(2(3(0(3(x1)))))))))))))))))) ->
 1(0(0(3(3(2(3(0(3(0(1(1(3(3(1(2(0(3(x1))))))))))))))))))
 1(0(0(2(1(3(2(3(2(0(2(2(3(1(3(1(0(2(x1)))))))))))))))))) ->
 2(2(1(2(0(1(1(3(0(0(3(2(3(3(2(0(1(2(x1))))))))))))))))))
 1(0(1(0(1(1(3(1(0(1(3(1(1(0(2(0(0(2(x1)))))))))))))))))) ->
 1(0(1(0(2(0(1(1(1(3(3(0(1(2(0(1(0(1(x1))))))))))))))))))
 1(0(2(1(2(3(3(1(2(0(2(1(3(1(1(2(2(1(x1)))))))))))))))))) ->
 1(1(3(2(1(0(1(1(1(2(3(2(2(1(2(3(2(0(x1))))))))))))))))))
 1(0(2(2(2(2(1(1(0(1(0(3(2(2(2(2(1(1(x1)))))))))))))))))) ->
 1(1(1(2(1(2(0(3(2(2(0(2(2(2(0(2(1(1(x1))))))))))))))))))
 1(0(2(3(1(1(1(0(0(1(0(1(1(2(3(2(0(1(x1)))))))))))))))))) ->
 1(1(1(0(1(1(2(0(0(2(0(3(1(1(3(2(0(1(x1))))))))))))))))))
 1(0(3(3(1(2(0(0(1(3(1(2(2(3(2(1(0(2(x1)))))))))))))))))) ->
 3(2(2(1(2(0(3(2(1(1(0(1(3(0(3(2(0(1(x1))))))))))))))))))
 1(1(0(2(0(3(3(3(1(2(1(2(3(1(1(0(1(2(x1)))))))))))))))))) ->
 1(1(0(3(3(2(1(0(3(1(2(1(1(1(0(2(2(3(x1))))))))))))))))))
 1(1(1(1(3(1(1(1(3(3(1(2(1(3(3(2(2(2(x1)))))))))))))))))) ->
 1(1(1(1(1(3(2(3(3(3(2(1(1(1(3(1(2(2(x1))))))))))))))))))
 1(1(1(3(3(3(2(2(1(1(0(1(0(2(0(2(3(3(x1)))))))))))))))))) ->
 2(3(1(1(2(0(1(2(0(3(2(0(1(3(1(1(3(3(x1))))))))))))))))))
 1(1(2(1(0(2(3(2(1(2(2(1(0(0(3(3(2(1(x1)))))))))))))))))) ->
 2(2(2(2(0(1(2(3(0(1(2(1(3(1(3(1(1(0(x1))))))))))))))))))
 1(1(3(3(3(1(2(3(1(2(1(1(3(3(1(1(0(2(x1)))))))))))))))))) ->
 1(3(0(2(1(1(1(3(3(1(3(1(3(2(3(1(2(1(x1))))))))))))))))))
 1(1(3(3(3(2(1(1(1(3(1(1(1(1(0(2(1(1(x1)))))))))))))))))) ->
 1(2(1(1(1(1(1(1(2(1(3(0(3(3(3(1(1(1(x1))))))))))))))))))
 1(2(0(0(1(3(2(1(0(1(2(0(3(1(0(1(3(1(x1)))))))))))))))))) ->
 1(2(2(1(0(0(3(1(3(2(0(3(0(1(0(1(1(1(x1))))))))))))))))))
 1(2(2(2(2(3(2(3(1(0(3(2(1(1(0(0(0(3(x1)))))))))))))))))) ->
 2(3(0(1(2(1(3(2(0(1(2(0(1(3(2(2(0(3(x1))))))))))))))))))
 1(2(3(1(1(0(2(2(3(3(0(2(1(2(1(0(3(3(x1)))))))))))))))))) ->
 2(1(2(3(0(3(3(2(1(2(0(3(2(0(1(1(1(3(x1))))))))))))))))))
 1(2(3(2(1(2(2(0(0(2(1(1(1(0(0(0(2(2(x1)))))))))))))))))) ->
 2(0(3(1(2(2(1(0(1(2(2(0(1(0(2(0(1(2(x1))))))))))))))))))
 1(3(1(0(1(3(3(1(1(0(2(3(1(3(3(3(3(1(x1)))))))))))))))))) ->
 1(0(3(3(3(1(3(1(2(3(3(1(3(1(1(3(0(1(x1))))))))))))))))))
 1(3(2(1(0(3(0(2(2(2(3(2(1(1(2(0(2(1(x1)))))))))))))))))) ->
 1(3(2(1(0(2(2(2(2(0(1(1(3(2(1(3(2(0(x1))))))))))))))))))
 1(3(3(0(3(3(0(2(2(1(0(1(0(1(1(3(3(3(x1)))))))))))))))))) ->
 1(3(1(3(2(1(0(0(3(0(3(3(0(1(3(2(1(3(x1))))))))))))))))))
 1(3(3(3(3(3(1(1(2(1(0(1(0(1(3(3(1(3(x1)))))))))))))))))) ->
 1(3(1(1(3(2(3(0(1(1(3(3(3(0(3(1(1(3(x1))))))))))))))))))
 2(0(0(1(2(3(0(1(0(1(0(0(0(2(0(1(0(2(x1)))))))))))))))))) ->
 2(0(0(1(1(1(2(0(0(3(2(0(0(0(0(1(0(2(x1))))))))))))))))))
 2(0(1(0(2(0(2(1(2(2(1(2(0(0(3(1(2(2(x1)))))))))))))))))) ->
 2(0(1(0(2(2(0(3(0(0(1(2(2(1(2(2(1(2(x1))))))))))))))))))
 2(1(0(0(0(0(1(0(3(3(3(2(1(1(0(2(0(1(x1)))))))))))))))))) ->
 2(0(1(1(0(3(0(3(1(0(1(2(2(0(3(0(1(0(x1))))))))))))))))))
 2(1(0(1(1(2(0(3(1(3(3(3(3(3(3(1(1(2(x1)))))))))))))))))) ->
 2(3(2(0(1(3(3(1(3(1(0(1(1(1(3(3(2(3(x1))))))))))))))))))
 2(1(0(1(3(1(0(2(0(1(3(1(1(1(1(3(1(3(x1)))))))))))))))))) ->
 2(0(3(0(3(0(1(2(1(1(1(1(1(1(1(3(1(3(x1))))))))))))))))))
 2(1(1(0(2(1(3(1(0(0(1(1(0(3(0(0(1(0(x1)))))))))))))))))) ->
 2(0(3(1(1(1(2(0(3(1(0(0(1(1(0(0(1(0(x1))))))))))))))))))
 2(1(1(2(2(3(0(2(3(1(2(1(2(0(2(0(0(3(x1)))))))))))))))))) ->
 2(2(2(2(2(0(1(1(3(2(0(2(1(0(3(0(1(3(x1))))))))))))))))))
 2(1(2(2(2(1(0(1(1(0(3(1(1(0(2(3(1(1(x1)))))))))))))))))) ->
 1(1(1(2(3(0(1(2(2(1(2(0(3(2(1(1(0(1(x1))))))))))))))))))
 2(2(1(1(2(2(1(1(3(3(3(1(0(0(0(1(3(3(x1)))))))))))))))))) ->
 2(3(0(0(1(2(3(3(1(1(3(0(1(1(1(2(2(3(x1))))))))))))))))))
 2(2(1(2(0(0(0(0(0(3(3(0(3(2(2(0(3(3(x1)))))))))))))))))) ->
 2(2(2(2(1(2(0(3(0(0(0(3(3(0(0(3(0(3(x1))))))))))))))))))
 2(2(2(0(2(2(2(1(3(2(3(1(2(0(2(2(2(1(x1)))))))))))))))))) ->
 2(2(3(2(2(2(0(1(2(2(2(2(0(3(1(2(2(1(x1))))))))))))))))))
 2(2(3(1(3(3(2(2(2(3(2(1(2(3(0(2(0(2(x1)))))))))))))))))) ->
 2(2(1(1(2(3(2(3(2(3(0(3(2(2(3(0(2(2(x1))))))))))))))))))
 2(2(3(2(1(3(2(3(1(2(0(0(2(2(1(0(0(2(x1)))))))))))))))))) ->
 2(2(2(2(2(0(1(1(0(3(0(3(2(2(0(1(2(3(x1))))))))))))))))))
 2(3(1(2(0(0(0(0(1(2(2(1(1(2(3(3(3(1(x1)))))))))))))))))) ->
 2(1(1(0(0(3(3(2(2(1(1(2(1(2(3(0(3(0(x1))))))))))))))))))
 2(3(1(2(3(0(1(2(1(0(0(3(3(3(0(3(0(1(x1)))))))))))))))))) ->
 2(3(2(1(1(3(0(3(0(2(1(3(0(0(3(1(3(0(x1))))))))))))))))))
 2(3(2(1(2(2(2(2(0(0(3(0(1(1(0(1(0(2(x1)))))))))))))))))) ->
 2(2(1(2(1(0(2(2(0(3(2(0(0(1(0(3(1(2(x1))))))))))))))))))
 2(3(2(3(2(2(0(2(0(0(1(3(3(1(3(2(2(3(x1)))))))))))))))))) ->
 2(2(0(3(1(3(2(3(2(2(3(3(0(1(2(0(3(2(x1))))))))))))))))))
 2(3(3(0(0(3(2(2(3(0(1(3(3(0(2(3(3(1(x1)))))))))))))))))) ->
 2(2(0(2(0(3(3(1(3(3(3(0(3(0(3(2(3(1(x1))))))))))))))))))
 2(3(3(2(3(1(2(3(1(1(2(3(1(2(2(1(1(2(x1)))))))))))))))))) ->
 1(2(1(1(1(1(3(2(3(3(2(2(3(2(1(3(2(2(x1))))))))))))))))))
 3(0(0(0(0(1(3(3(1(0(0(0(0(2(0(3(3(3(x1)))))))))))))))))) ->
 3(0(3(3(0(0(0(0(3(1(2(3(0(1(0(0(0(3(x1))))))))))))))))))
 3(0(0(0(3(3(1(1(3(2(0(0(1(1(0(2(3(0(x1)))))))))))))))))) ->
 3(0(1(0(2(0(3(0(3(3(2(0(0(1(3(0(1(1(x1))))))))))))))))))
 3(0(0(3(1(0(2(0(3(0(0(2(1(0(0(0(2(3(x1)))))))))))))))))) ->
 3(0(0(2(0(1(0(2(0(2(0(0(3(0(1(3(0(3(x1))))))))))))))))))
 3(0(1(3(0(3(3(2(2(3(3(0(3(1(3(3(3(1(x1)))))))))))))))))) ->
 3(1(3(1(3(3(1(3(3(2(0(3(3(3(0(3(2(0(x1))))))))))))))))))
 3(0(2(0(2(1(2(0(1(1(3(0(0(0(3(0(2(3(x1)))))))))))))))))) ->
 3(0(0(3(2(0(2(2(0(0(1(1(2(3(1(0(0(3(x1))))))))))))))))))
 3(0(2(3(3(1(1(3(2(3(3(1(1(3(1(1(0(2(x1)))))))))))))))))) ->
 3(2(3(1(0(3(0(2(1(1(3(1(1(3(1(3(2(3(x1))))))))))))))))))
 3(1(0(0(1(1(3(3(1(1(2(1(3(2(2(2(2(2(x1)))))))))))))))))) ->
 3(2(1(0(3(0(1(2(2(1(1(1(1(3(2(3(2(2(x1))))))))))))))))))
 3(1(0(3(3(1(0(2(2(0(2(1(3(3(3(3(2(3(x1)))))))))))))))))) ->
 3(3(2(3(3(2(0(1(3(0(0(1(1(2(3(2(3(3(x1))))))))))))))))))
 3(1(1(0(0(2(1(2(1(3(2(3(0(1(1(0(1(2(x1)))))))))))))))))) ->
 3(2(0(3(2(0(1(0(1(2(1(1(3(0(2(1(1(1(x1))))))))))))))))))
 3(1(1(0(2(1(1(2(0(0(0(2(2(3(2(3(2(0(x1)))))))))))))))))) ->
 3(2(1(0(2(2(2(0(1(0(3(2(1(3(2(0(1(0(x1))))))))))))))))))
 3(1(1(2(3(3(0(3(0(0(2(2(1(3(1(2(1(2(x1)))))))))))))))))) ->
 3(2(3(2(1(3(1(1(0(1(2(0(2(3(1(3(0(2(x1))))))))))))))))))
 3(1(2(0(0(2(1(2(2(3(0(0(0(1(1(1(3(1(x1)))))))))))))))))) ->
 3(2(0(1(1(2(2(3(1(0(0(0(1(1(2(3(0(1(x1))))))))))))))))))
 3(1(3(1(0(2(1(2(3(3(2(0(0(0(0(3(3(3(x1)))))))))))))))))) ->
 3(2(0(1(0(1(0(3(0(3(2(1(2(0(3(3(3(3(x1))))))))))))))))))
 3(2(0(0(2(1(3(3(2(2(3(0(3(0(3(2(3(2(x1)))))))))))))))))) ->
 3(0(3(2(1(2(3(2(0(3(0(3(2(3(0(3(2(2(x1))))))))))))))))))
 3(2(2(3(1(2(2(0(2(1(2(1(1(1(2(2(1(2(x1)))))))))))))))))) ->
 3(2(0(1(2(1(2(1(1(2(2(1(2(2(2(3(1(2(x1))))))))))))))))))
 3(3(0(0(0(3(2(3(2(3(2(0(0(1(3(1(0(1(x1)))))))))))))))))) ->
 3(3(0(1(3(3(0(2(0(3(0(1(0(3(2(2(0(1(x1))))))))))))))))))
 3(3(0(2(2(0(2(2(2(0(2(3(3(3(1(3(1(2(x1)))))))))))))))))) ->
 3(3(3(0(2(1(2(1(3(2(0(2(0(2(3(2(2(3(x1))))))))))))))))))
 3(3(0(3(0(3(2(2(0(2(3(3(3(3(3(3(0(2(x1)))))))))))))))))) ->
 3(3(2(3(0(3(3(3(0(2(3(0(3(0(2(3(2(3(x1))))))))))))))))))
 3(3(2(1(3(1(0(0(0(3(2(1(2(1(2(3(1(2(x1)))))))))))))))))) ->
 3(3(3(0(0(1(2(3(1(0(1(3(1(1(2(2(2(2(x1))))))))))))))))))
 3(3(2(3(1(2(3(3(1(2(2(0(1(2(0(0(0(1(x1)))))))))))))))))) ->
 3(0(3(0(2(1(2(0(3(3(2(0(2(2(3(1(1(1(x1))))))))))))))))))
 3(3(2(3(2(0(2(1(0(0(0(3(0(1(1(3(0(2(x1)))))))))))))))))) ->
 3(2(0(3(1(0(3(0(3(0(2(2(0(1(2(1(0(3(x1))))))))))))))))))
 3(3(3(0(2(1(0(0(2(1(0(1(0(1(0(2(0(0(x1)))))))))))))))))) ->
 3(2(1(0(1(1(2(0(0(3(3(0(1(2(0(0(0(0(x1))))))))))))))))))
 3(3(3(1(0(1(3(2(0(3(1(0(2(0(1(1(0(1(x1)))))))))))))))))) ->
 3(1(3(3(0(2(1(3(0(0(1(0(1(1(2(1(3(0(x1))))))))))))))))))
 3(3(3(1(3(3(2(3(3(0(2(1(0(1(3(1(3(3(x1)))))))))))))))))) ->
 3(3(3(1(0(3(2(3(1(3(3(2(1(0(3(1(3(3(x1))))))))))))))))))

Proof:
 Open