MAYBE

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

Proof:
 Open