MAYBE

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

Proof:
 Open