MAYBE

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

Proof:
 Open