MAYBE Termination Proof

Termination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

0(x0) → 1(1(x0))
0(0(x0)) → 1(1(2(x0)))
2(0(x0)) → 1(1(0(x0)))
2(0(0(x0))) → 0(1(2(1(1(x0)))))
2(2(1(x0))) → 1(1(0(1(1(x0)))))
0(2(0(0(x0)))) → 0(2(1(1(1(1(1(1(1(1(x0))))))))))
0(0(2(0(2(x0))))) → 1(2(2(1(1(2(2(1(1(x0)))))))))
0(2(0(2(0(0(x0)))))) → 0(1(2(2(1(2(0(x0)))))))
2(1(0(1(2(0(0(x0))))))) → 1(1(1(0(1(2(2(1(1(x0)))))))))
2(2(0(0(2(0(0(x0))))))) → 2(0(1(1(0(0(2(1(1(x0)))))))))
2(2(0(2(1(0(1(x0))))))) → 0(1(0(1(2(1(1(2(1(1(x0))))))))))
0(0(0(0(2(0(1(2(x0)))))))) → 1(1(1(2(1(1(1(0(0(0(2(x0)))))))))))
0(0(2(1(0(2(2(1(x0)))))))) → 1(1(0(1(0(2(1(1(1(0(x0))))))))))
2(0(2(1(1(2(2(0(x0)))))))) → 2(0(0(2(2(1(2(1(x0))))))))
2(1(2(0(1(0(2(2(x0)))))))) → 2(1(0(1(1(1(2(1(0(x0)))))))))
0(2(0(1(2(0(1(1(2(x0))))))))) → 1(2(2(1(1(1(2(2(1(0(x0))))))))))
1(1(2(2(0(1(0(1(1(x0))))))))) → 1(1(1(0(1(1(0(1(1(1(1(x0)))))))))))
2(1(0(1(2(1(2(2(2(x0))))))))) → 1(1(0(1(0(0(1(1(1(1(2(x0)))))))))))
2(2(0(2(1(0(1(0(1(x0))))))))) → 2(1(1(1(0(2(0(2(0(x0)))))))))
0(0(1(0(2(2(0(1(2(0(x0)))))))))) → 2(2(2(1(1(1(1(2(2(1(2(2(2(1(2(x0)))))))))))))))
0(1(1(0(0(2(0(1(2(2(x0)))))))))) → 1(1(2(1(1(2(1(1(0(0(0(2(1(x0)))))))))))))
1(0(1(1(0(2(2(0(2(0(x0)))))))))) → 1(1(0(2(2(1(0(2(0(0(x0))))))))))
1(0(1(2(2(0(0(2(2(1(x0)))))))))) → 1(0(1(2(0(1(0(1(1(1(1(2(x0))))))))))))
2(0(1(0(0(1(0(0(2(2(x0)))))))))) → 1(2(2(1(1(2(2(0(2(0(2(1(1(x0)))))))))))))
0(0(0(1(2(1(2(1(2(0(1(x0))))))))))) → 1(2(2(1(0(0(1(1(2(2(1(2(x0))))))))))))
0(0(2(0(0(1(0(1(1(1(2(x0))))))))))) → 1(2(1(1(1(0(2(1(0(1(2(2(1(x0)))))))))))))
0(0(2(0(2(2(2(2(2(2(0(x0))))))))))) → 0(2(0(1(0(0(1(1(1(1(2(1(x0))))))))))))
0(1(2(0(2(1(0(0(0(0(1(x0))))))))))) → 2(2(1(2(0(1(2(1(2(0(1(2(x0))))))))))))
0(2(0(2(2(0(2(0(0(0(2(x0))))))))))) → 0(1(1(0(2(2(1(1(1(0(1(2(0(2(x0))))))))))))))
1(2(2(2(2(0(2(1(0(0(0(x0))))))))))) → 2(1(1(2(0(1(0(0(1(0(1(1(x0))))))))))))
0(1(0(1(0(2(1(1(2(0(2(0(x0)))))))))))) → 1(1(1(1(0(2(1(1(2(1(2(2(2(2(1(1(x0))))))))))))))))
0(1(1(2(0(2(0(2(2(2(1(0(x0)))))))))))) → 2(0(1(0(0(1(1(0(1(1(0(2(0(x0)))))))))))))
0(1(1(2(2(1(1(2(2(0(0(0(x0)))))))))))) → 2(2(1(1(2(1(1(1(2(1(1(0(2(1(x0))))))))))))))
0(1(2(0(1(1(0(1(2(2(0(0(x0)))))))))))) → 1(1(1(1(0(1(2(0(0(2(1(0(2(1(x0))))))))))))))
0(1(2(2(0(0(1(2(2(0(0(0(x0)))))))))))) → 1(1(2(2(2(2(0(2(1(2(1(0(1(x0)))))))))))))
0(1(2(2(0(1(1(0(2(0(0(0(x0)))))))))))) → 1(2(1(2(1(2(0(2(0(2(1(1(0(x0)))))))))))))
2(1(0(0(0(0(2(0(0(0(2(0(x0)))))))))))) → 1(2(1(2(2(0(2(2(1(2(1(1(0(1(1(x0)))))))))))))))
2(0(2(0(1(2(2(0(2(1(0(0(0(x0))))))))))))) → 1(1(1(1(2(0(1(0(1(0(2(0(1(1(2(1(x0))))))))))))))))
2(2(2(2(0(0(1(2(2(1(1(0(0(x0))))))))))))) → 2(2(2(0(0(2(0(1(1(0(1(1(1(1(1(x0)))))))))))))))
0(0(1(0(1(1(1(0(1(0(2(0(0(1(x0)))))))))))))) → 1(2(1(1(1(1(0(1(1(0(0(2(1(0(0(0(x0))))))))))))))))
0(2(2(1(0(1(0(2(1(2(2(1(1(2(x0)))))))))))))) → 2(1(1(2(2(1(0(1(2(1(2(1(2(1(0(x0)))))))))))))))
0(2(2(0(1(0(0(2(2(2(1(2(2(2(2(x0))))))))))))))) → 2(2(1(0(2(1(2(2(0(0(0(1(0(0(1(1(x0))))))))))))))))
1(0(0(0(2(1(0(0(0(2(0(2(2(0(2(x0))))))))))))))) → 1(1(1(0(0(2(1(0(1(2(1(0(0(0(0(2(x0))))))))))))))))
1(0(1(2(0(1(1(0(2(1(0(2(0(1(0(x0))))))))))))))) → 1(0(0(1(1(1(2(1(0(2(0(1(0(1(1(1(0(x0)))))))))))))))))
0(2(1(0(0(1(0(2(2(0(0(2(0(0(2(1(x0)))))))))))))))) → 0(1(2(1(2(0(0(1(1(2(2(2(0(1(1(2(2(2(1(2(x0))))))))))))))))))))
2(0(2(0(2(2(0(2(0(1(0(0(0(0(1(2(x0)))))))))))))))) → 1(1(2(1(0(0(2(1(1(2(1(2(1(1(2(1(2(1(2(2(0(2(x0))))))))))))))))))))))
2(0(2(2(2(2(1(2(0(1(0(1(0(2(2(1(x0)))))))))))))))) → 2(1(2(1(2(2(2(0(0(1(2(2(1(0(0(2(x0))))))))))))))))
0(1(0(2(0(1(2(2(0(1(0(0(2(0(1(2(2(x0))))))))))))))))) → 1(2(2(1(2(1(2(2(1(0(0(0(0(0(0(0(2(x0)))))))))))))))))
0(1(0(2(2(0(2(2(0(2(1(0(2(1(0(0(2(x0))))))))))))))))) → 1(1(1(0(1(2(2(0(2(2(1(2(2(0(1(0(1(0(x0))))))))))))))))))
0(2(0(2(2(2(0(1(0(2(0(2(0(2(1(2(0(x0))))))))))))))))) → 1(0(1(1(0(2(2(0(1(2(1(0(0(1(2(1(0(1(x0))))))))))))))))))
1(1(0(1(0(2(1(0(2(0(1(2(2(2(2(1(1(x0))))))))))))))))) → 1(1(2(2(1(1(0(0(2(0(0(1(1(0(2(2(1(1(x0))))))))))))))))))
1(2(2(2(0(2(1(2(0(1(0(2(1(0(2(1(0(x0))))))))))))))))) → 1(1(1(2(1(0(1(1(2(2(0(1(2(1(2(1(0(0(2(1(2(1(2(x0)))))))))))))))))))))))
2(1(2(0(1(2(1(0(0(2(0(0(2(0(0(1(2(x0))))))))))))))))) → 1(2(1(2(1(1(2(0(2(0(2(1(1(1(1(0(2(1(1(x0)))))))))))))))))))
0(2(0(2(2(1(0(1(2(0(0(2(1(0(2(2(1(1(x0)))))))))))))))))) → 1(1(1(0(2(0(1(2(0(2(2(0(1(0(1(0(0(1(1(x0)))))))))))))))))))
0(2(2(2(0(1(0(2(0(1(0(0(0(2(2(2(2(0(x0)))))))))))))))))) → 2(1(2(1(2(0(0(0(2(0(0(1(1(0(2(1(2(0(0(2(x0))))))))))))))))))))
0(1(0(0(0(0(0(2(2(1(0(2(2(0(2(1(2(2(1(x0))))))))))))))))))) → 2(1(2(1(1(1(2(1(1(0(2(2(0(1(0(0(2(0(2(1(1(0(1(1(2(1(x0))))))))))))))))))))))))))
0(1(0(2(0(2(2(1(2(2(1(0(2(0(1(0(2(2(2(x0))))))))))))))))))) → 0(1(0(2(2(1(1(0(1(2(0(2(1(2(1(2(1(1(1(1(x0))))))))))))))))))))
1(0(1(1(2(0(1(1(0(0(2(1(0(0(2(2(0(0(0(x0))))))))))))))))))) → 2(1(1(0(1(1(2(1(2(2(2(2(1(1(1(1(2(1(1(2(0(0(2(1(x0))))))))))))))))))))))))
1(0(1(2(0(1(0(2(2(1(0(1(0(0(2(2(2(0(0(x0))))))))))))))))))) → 1(0(2(1(1(1(1(0(2(1(0(1(2(0(0(2(1(1(0(0(1(1(0(2(x0))))))))))))))))))))))))
1(2(0(2(2(0(0(1(0(0(2(0(2(2(1(0(1(0(2(x0))))))))))))))))))) → 2(2(1(2(1(0(2(1(2(2(1(2(2(0(2(2(0(2(0(0(1(1(1(x0)))))))))))))))))))))))
2(2(2(2(0(0(1(0(1(1(1(2(0(2(0(2(2(0(0(x0))))))))))))))))))) → 2(0(0(0(1(1(0(2(2(2(1(2(0(0(1(1(2(1(1(1(2(1(2(x0)))))))))))))))))))))))
0(0(1(0(0(0(2(2(1(0(2(1(2(1(2(2(2(0(0(2(x0)))))))))))))))))))) → 0(0(2(0(2(1(1(2(0(0(1(1(2(1(1(1(2(1(1(1(1(0(1(x0)))))))))))))))))))))))
0(1(2(1(0(1(0(2(2(2(2(1(0(2(1(0(1(1(1(1(x0)))))))))))))))))))) → 0(1(1(1(1(0(1(1(2(0(0(2(2(0(1(2(1(1(2(2(x0))))))))))))))))))))
1(1(0(0(1(2(1(0(0(1(1(2(1(0(0(0(1(2(1(2(x0)))))))))))))))))))) → 2(2(1(2(1(2(1(0(0(1(1(1(2(1(1(1(1(1(1(1(1(2(1(x0)))))))))))))))))))))))
1(1(0(2(2(0(0(0(2(1(2(1(0(1(0(0(0(0(0(1(x0)))))))))))))))))))) → 1(2(1(1(2(1(0(0(1(2(1(2(1(2(2(2(1(0(2(1(0(0(x0))))))))))))))))))))))
0(0(1(2(2(2(1(2(2(0(0(0(2(1(2(1(2(1(2(2(2(x0))))))))))))))))))))) → 1(1(2(1(1(1(1(2(1(1(0(2(1(0(0(2(1(2(1(2(1(0(0(x0)))))))))))))))))))))))
0(0(2(2(0(1(2(0(0(0(1(2(2(2(0(0(1(1(0(2(0(x0))))))))))))))))))))) → 1(2(1(0(1(1(1(2(1(2(0(2(1(1(2(0(2(2(1(2(0(0(1(1(0(2(x0))))))))))))))))))))))))))
0(2(2(0(1(0(0(0(2(2(1(0(1(2(0(1(0(1(0(0(0(x0))))))))))))))))))))) → 0(0(2(1(1(2(1(0(2(0(1(2(1(0(2(1(1(2(2(0(0(1(0(2(x0))))))))))))))))))))))))
0(2(2(0(1(2(2(2(2(1(2(0(2(1(0(1(0(2(0(1(2(x0))))))))))))))))))))) → 0(2(0(0(2(1(1(0(1(1(1(0(2(2(2(1(1(1(1(2(0(0(0(x0)))))))))))))))))))))))
1(0(0(0(1(2(1(2(0(2(0(0(1(0(0(0(1(2(1(0(2(x0))))))))))))))))))))) → 2(2(2(2(1(1(2(1(0(1(0(2(2(1(0(0(1(1(1(1(0(1(0(x0)))))))))))))))))))))))
1(0(2(1(1(1(1(0(0(2(2(0(1(0(1(0(2(2(0(0(0(x0))))))))))))))))))))) → 1(1(1(1(0(2(1(2(2(1(1(1(0(2(2(1(2(2(1(0(1(2(x0))))))))))))))))))))))
2(0(0(2(2(2(1(1(2(2(0(2(1(0(0(0(2(2(1(0(1(x0))))))))))))))))))))) → 2(1(1(2(1(1(1(0(1(2(2(1(2(0(0(0(2(0(0(1(2(0(x0))))))))))))))))))))))
2(0(2(2(2(0(0(1(2(2(1(1(2(0(0(0(2(0(0(0(2(x0))))))))))))))))))))) → 1(1(1(0(1(2(2(1(2(2(2(1(1(1(1(1(1(1(0(2(1(0(1(0(x0))))))))))))))))))))))))
2(1(2(1(1(2(0(0(1(1(0(1(1(2(1(1(1(1(0(1(2(x0))))))))))))))))))))) → 1(1(1(1(2(1(0(1(0(1(2(2(1(2(1(1(1(0(0(1(2(x0)))))))))))))))))))))
2(2(0(0(2(1(0(1(0(0(0(0(0(1(0(0(2(0(0(1(1(x0))))))))))))))))))))) → 2(0(2(0(2(0(0(0(2(2(1(1(2(2(2(1(1(1(1(1(2(1(2(x0)))))))))))))))))))))))
2(2(0(2(1(1(0(1(2(0(1(1(2(0(2(0(1(0(2(0(1(x0))))))))))))))))))))) → 2(1(2(1(0(1(1(1(1(0(2(2(2(1(2(2(1(2(1(1(0(2(x0))))))))))))))))))))))
0(0(1(2(2(0(1(1(2(0(1(0(0(0(0(1(0(1(2(2(2(1(x0)))))))))))))))))))))) → 1(1(1(1(2(2(2(0(2(0(2(2(1(0(2(0(2(1(2(1(2(1(1(1(0(1(x0))))))))))))))))))))))))))
1(0(1(1(0(0(1(1(1(0(2(2(0(1(0(0(1(2(0(0(2(0(x0)))))))))))))))))))))) → 1(1(1(2(2(0(2(1(2(0(2(0(0(0(1(2(1(2(1(2(0(2(1(x0)))))))))))))))))))))))
2(0(0(1(1(2(2(2(2(1(2(0(1(2(0(2(2(1(2(2(0(2(x0)))))))))))))))))))))) → 1(1(1(0(0(2(2(2(1(2(2(0(1(1(1(1(2(1(0(1(1(2(0(2(2(x0)))))))))))))))))))))))))
2(0(1(2(2(0(1(0(0(0(2(1(2(1(2(0(1(1(2(0(1(0(x0)))))))))))))))))))))) → 0(2(1(1(0(2(1(1(0(1(1(2(2(0(1(2(2(1(0(1(1(1(0(x0)))))))))))))))))))))))
2(2(1(0(1(1(2(0(2(1(1(0(0(1(2(1(2(2(2(0(2(1(x0)))))))))))))))))))))) → 2(1(1(2(1(2(0(2(1(1(1(1(2(1(1(2(1(1(0(1(1(2(2(1(1(x0)))))))))))))))))))))))))
2(2(2(0(0(1(0(2(0(2(0(0(1(2(1(2(1(2(0(1(1(1(x0)))))))))))))))))))))) → 1(1(2(1(2(1(2(1(2(1(0(2(0(1(1(0(1(0(0(2(0(2(1(2(1(x0)))))))))))))))))))))))))
0(0(1(2(0(0(1(0(0(2(0(1(0(1(2(0(2(0(0(2(2(0(2(x0))))))))))))))))))))))) → 0(0(1(0(1(2(2(0(1(0(0(2(0(1(1(1(0(1(2(1(2(0(0(1(0(1(x0))))))))))))))))))))))))))
2(2(1(2(0(0(0(0(1(2(1(0(1(0(2(0(1(0(0(1(2(0(2(x0))))))))))))))))))))))) → 2(1(1(2(2(2(2(1(0(1(2(0(1(1(1(1(1(2(1(2(1(1(0(2(1(1(0(0(2(x0)))))))))))))))))))))))))))))
1(2(0(2(1(2(0(0(0(0(0(0(2(2(1(0(2(2(0(2(1(0(0(1(x0)))))))))))))))))))))))) → 1(0(1(0(0(2(2(1(1(2(0(2(2(0(0(2(0(1(0(1(1(1(1(2(2(2(1(x0)))))))))))))))))))))))))))
1(2(2(1(2(0(1(2(0(1(2(1(0(0(0(2(2(2(0(2(2(0(2(1(x0)))))))))))))))))))))))) → 2(1(0(2(0(2(1(1(1(1(2(0(0(1(0(2(1(0(2(0(2(0(1(1(2(x0)))))))))))))))))))))))))
2(1(1(2(0(0(0(2(0(2(2(2(2(0(1(0(1(0(2(2(1(1(1(2(x0)))))))))))))))))))))))) → 2(1(1(2(1(1(2(1(2(1(2(0(1(1(0(0(0(1(1(1(2(1(2(1(1(x0)))))))))))))))))))))))))
0(1(0(1(1(0(1(1(0(2(2(0(2(1(0(0(2(0(0(1(2(0(2(0(2(x0))))))))))))))))))))))))) → 1(1(2(1(1(1(1(2(0(2(0(2(1(2(2(0(1(1(2(0(1(1(0(2(2(2(0(x0)))))))))))))))))))))))))))
0(1(2(2(1(0(0(2(1(1(2(0(1(0(2(0(1(0(1(2(2(0(1(1(0(x0))))))))))))))))))))))))) → 0(1(1(1(2(1(1(2(2(0(0(0(0(1(1(2(0(0(0(2(1(2(1(1(0(1(x0))))))))))))))))))))))))))
1(0(1(0(0(0(2(0(1(2(0(2(0(2(0(1(0(2(2(0(0(1(0(1(1(x0))))))))))))))))))))))))) → 1(2(0(0(2(0(1(0(1(0(2(2(1(1(0(0(0(1(2(1(1(1(1(0(2(1(x0))))))))))))))))))))))))))
1(1(0(2(0(1(2(1(0(0(1(0(0(2(1(0(2(0(1(0(0(0(1(0(1(x0))))))))))))))))))))))))) → 2(1(0(2(0(0(1(1(2(2(1(2(0(2(2(1(2(1(2(2(1(0(2(1(2(1(x0))))))))))))))))))))))))))
0(0(0(1(0(2(1(2(0(1(2(0(0(2(1(0(2(0(2(2(2(2(0(2(0(0(x0)))))))))))))))))))))))))) → 0(2(1(0(0(1(0(1(0(0(1(0(1(0(0(2(2(0(1(1(1(1(1(0(1(1(0(2(0(x0)))))))))))))))))))))))))))))
0(0(1(2(2(0(1(2(0(0(0(2(0(2(1(2(0(0(0(2(0(2(2(2(0(1(x0)))))))))))))))))))))))))) → 1(1(0(1(2(1(2(1(1(1(0(0(1(1(2(2(0(2(0(0(2(0(0(1(1(2(1(x0)))))))))))))))))))))))))))
0(2(0(2(2(2(0(1(1(2(2(2(0(0(1(2(0(2(2(1(2(0(0(1(2(2(x0)))))))))))))))))))))))))) → 0(1(1(2(1(0(2(1(1(1(1(2(1(1(1(2(1(1(2(0(2(0(2(2(1(2(1(2(0(x0)))))))))))))))))))))))))))))
2(1(2(2(0(0(2(0(0(0(1(1(2(0(1(1(2(2(2(0(0(0(2(1(2(1(x0)))))))))))))))))))))))))) → 1(1(0(0(0(1(1(0(2(0(1(2(1(1(1(1(2(1(1(1(1(2(1(0(1(2(2(1(x0))))))))))))))))))))))))))))
2(2(0(2(1(2(0(2(0(2(0(0(0(2(1(2(2(0(1(0(1(0(1(0(1(0(x0)))))))))))))))))))))))))) → 1(1(0(1(2(1(0(2(2(2(0(1(2(1(1(1(2(2(2(2(1(2(2(1(0(2(2(2(0(x0)))))))))))))))))))))))))))))
2(2(2(0(0(1(0(1(2(0(0(0(2(0(2(2(0(1(0(0(2(1(2(2(2(2(x0)))))))))))))))))))))))))) → 2(1(2(1(0(1(2(0(1(0(2(2(0(1(1(2(0(1(2(2(2(2(0(0(0(1(2(x0)))))))))))))))))))))))))))
2(2(2(2(0(1(1(2(0(2(0(1(1(2(0(1(2(1(1(2(2(1(2(1(2(2(x0)))))))))))))))))))))))))) → 2(0(0(1(1(2(2(1(1(1(1(0(1(2(1(2(1(1(2(1(2(2(1(0(2(1(1(0(2(x0)))))))))))))))))))))))))))))
0(1(0(0(2(0(0(2(2(2(0(1(2(1(1(1(2(0(1(1(0(0(0(1(0(1(0(x0))))))))))))))))))))))))))) → 0(1(0(0(1(0(1(2(0(2(0(0(2(0(1(2(2(1(1(1(0(1(2(1(0(0(0(x0)))))))))))))))))))))))))))
0(1(1(2(0(0(2(2(0(0(1(2(2(2(1(2(2(2(2(0(2(0(2(0(0(0(1(x0))))))))))))))))))))))))))) → 0(1(0(1(1(2(0(1(0(1(1(1(0(2(2(0(1(1(0(0(0(2(0(1(1(1(0(0(x0))))))))))))))))))))))))))))
1(0(1(1(1(2(2(1(0(1(0(2(1(1(0(2(1(0(1(2(1(0(2(2(1(0(0(x0))))))))))))))))))))))))))) → 2(2(2(2(1(2(1(1(1(2(2(2(1(2(2(2(1(1(0(1(1(2(1(0(2(2(1(1(x0))))))))))))))))))))))))))))
2(0(2(0(1(2(0(1(0(2(2(2(0(1(1(0(0(1(1(2(2(2(1(0(1(2(1(x0))))))))))))))))))))))))))) → 2(1(0(1(1(1(1(2(1(2(0(2(0(1(2(2(0(2(1(2(1(1(2(0(2(2(1(0(x0))))))))))))))))))))))))))))
2(2(2(0(2(1(2(2(1(0(1(1(1(0(1(2(1(1(2(1(2(0(1(0(2(2(1(x0))))))))))))))))))))))))))) → 0(1(0(1(2(1(2(2(1(2(1(2(1(0(2(1(2(2(1(1(2(1(1(0(2(0(2(x0)))))))))))))))))))))))))))
0(0(0(0(0(1(0(2(2(2(0(0(2(0(1(0(1(2(1(1(0(1(0(2(0(0(1(0(x0)))))))))))))))))))))))))))) → 1(0(2(1(2(1(2(1(1(2(1(1(1(1(1(1(1(1(0(2(2(1(2(1(1(1(0(1(0(1(x0))))))))))))))))))))))))))))))
1(2(2(1(1(2(2(1(1(2(1(2(2(0(0(1(2(1(0(1(1(0(1(0(0(2(2(0(x0)))))))))))))))))))))))))))) → 1(2(1(2(1(0(1(2(2(2(1(2(0(0(0(2(1(0(0(1(1(1(0(0(1(1(1(1(1(0(x0))))))))))))))))))))))))))))))
2(0(1(1(1(0(0(0(0(2(0(1(2(0(1(0(1(2(2(0(2(2(2(0(2(1(0(0(x0)))))))))))))))))))))))))))) → 1(1(0(1(1(2(2(1(2(1(0(2(0(0(2(1(1(1(1(2(0(1(0(1(1(1(1(2(1(1(x0))))))))))))))))))))))))))))))
2(2(2(2(2(1(0(2(2(0(2(1(0(0(1(1(2(1(1(1(1(2(2(0(0(2(2(0(x0)))))))))))))))))))))))))))) → 2(1(1(0(1(1(2(2(2(2(2(1(1(1(0(2(1(0(1(1(0(2(2(1(0(2(1(1(1(2(x0))))))))))))))))))))))))))))))
0(0(1(1(2(2(0(1(1(0(1(2(2(0(2(0(2(1(0(0(1(1(0(1(0(0(0(1(1(x0))))))))))))))))))))))))))))) → 0(1(2(0(1(1(0(1(1(0(2(1(2(1(1(0(2(1(1(2(2(1(1(2(1(2(2(2(0(2(x0))))))))))))))))))))))))))))))
0(2(2(1(0(1(2(0(1(0(1(2(0(1(1(0(1(2(0(0(2(0(1(2(0(1(1(2(1(x0))))))))))))))))))))))))))))) → 0(1(2(1(2(1(2(2(2(1(1(0(0(1(2(2(2(2(2(2(2(1(0(0(0(1(2(0(0(1(x0))))))))))))))))))))))))))))))
2(1(1(2(1(1(1(0(2(1(1(2(1(1(2(2(1(1(2(0(1(0(1(2(0(1(0(0(1(x0))))))))))))))))))))))))))))) → 2(2(1(1(1(0(1(2(1(0(1(2(1(1(1(2(1(0(2(0(1(2(1(0(0(1(1(2(1(x0)))))))))))))))))))))))))))))

Proof

1 Termination Assumption

We assume termination of the following TRS
0(x0) → 1(1(x0))
0(0(x0)) → 1(1(2(x0)))
2(0(x0)) → 1(1(0(x0)))
2(0(0(x0))) → 0(1(2(1(1(x0)))))
2(2(1(x0))) → 1(1(0(1(1(x0)))))
0(2(0(0(x0)))) → 0(2(1(1(1(1(1(1(1(1(x0))))))))))
0(0(2(0(2(x0))))) → 1(2(2(1(1(2(2(1(1(x0)))))))))
0(2(0(2(0(0(x0)))))) → 0(1(2(2(1(2(0(x0)))))))
2(1(0(1(2(0(0(x0))))))) → 1(1(1(0(1(2(2(1(1(x0)))))))))
2(2(0(0(2(0(0(x0))))))) → 2(0(1(1(0(0(2(1(1(x0)))))))))
2(2(0(2(1(0(1(x0))))))) → 0(1(0(1(2(1(1(2(1(1(x0))))))))))
0(0(0(0(2(0(1(2(x0)))))))) → 1(1(1(2(1(1(1(0(0(0(2(x0)))))))))))
0(0(2(1(0(2(2(1(x0)))))))) → 1(1(0(1(0(2(1(1(1(0(x0))))))))))
2(0(2(1(1(2(2(0(x0)))))))) → 2(0(0(2(2(1(2(1(x0))))))))
2(1(2(0(1(0(2(2(x0)))))))) → 2(1(0(1(1(1(2(1(0(x0)))))))))
0(2(0(1(2(0(1(1(2(x0))))))))) → 1(2(2(1(1(1(2(2(1(0(x0))))))))))
1(1(2(2(0(1(0(1(1(x0))))))))) → 1(1(1(0(1(1(0(1(1(1(1(x0)))))))))))
2(1(0(1(2(1(2(2(2(x0))))))))) → 1(1(0(1(0(0(1(1(1(1(2(x0)))))))))))
2(2(0(2(1(0(1(0(1(x0))))))))) → 2(1(1(1(0(2(0(2(0(x0)))))))))
0(0(1(0(2(2(0(1(2(0(x0)))))))))) → 2(2(2(1(1(1(1(2(2(1(2(2(2(1(2(x0)))))))))))))))
0(1(1(0(0(2(0(1(2(2(x0)))))))))) → 1(1(2(1(1(2(1(1(0(0(0(2(1(x0)))))))))))))
1(0(1(1(0(2(2(0(2(0(x0)))))))))) → 1(1(0(2(2(1(0(2(0(0(x0))))))))))
1(0(1(2(2(0(0(2(2(1(x0)))))))))) → 1(0(1(2(0(1(0(1(1(1(1(2(x0))))))))))))
2(0(1(0(0(1(0(0(2(2(x0)))))))))) → 1(2(2(1(1(2(2(0(2(0(2(1(1(x0)))))))))))))
0(0(0(1(2(1(2(1(2(0(1(x0))))))))))) → 1(2(2(1(0(0(1(1(2(2(1(2(x0))))))))))))
0(0(2(0(0(1(0(1(1(1(2(x0))))))))))) → 1(2(1(1(1(0(2(1(0(1(2(2(1(x0)))))))))))))
0(0(2(0(2(2(2(2(2(2(0(x0))))))))))) → 0(2(0(1(0(0(1(1(1(1(2(1(x0))))))))))))
0(1(2(0(2(1(0(0(0(0(1(x0))))))))))) → 2(2(1(2(0(1(2(1(2(0(1(2(x0))))))))))))
0(2(0(2(2(0(2(0(0(0(2(x0))))))))))) → 0(1(1(0(2(2(1(1(1(0(1(2(0(2(x0))))))))))))))
1(2(2(2(2(0(2(1(0(0(0(x0))))))))))) → 2(1(1(2(0(1(0(0(1(0(1(1(x0))))))))))))
0(1(0(1(0(2(1(1(2(0(2(0(x0)))))))))))) → 1(1(1(1(0(2(1(1(2(1(2(2(2(2(1(1(x0))))))))))))))))
0(1(1(2(0(2(0(2(2(2(1(0(x0)))))))))))) → 2(0(1(0(0(1(1(0(1(1(0(2(0(x0)))))))))))))
0(1(1(2(2(1(1(2(2(0(0(0(x0)))))))))))) → 2(2(1(1(2(1(1(1(2(1(1(0(2(1(x0))))))))))))))
0(1(2(0(1(1(0(1(2(2(0(0(x0)))))))))))) → 1(1(1(1(0(1(2(0(0(2(1(0(2(1(x0))))))))))))))
0(1(2(2(0(0(1(2(2(0(0(0(x0)))))))))))) → 1(1(2(2(2(2(0(2(1(2(1(0(1(x0)))))))))))))
0(1(2(2(0(1(1(0(2(0(0(0(x0)))))))))))) → 1(2(1(2(1(2(0(2(0(2(1(1(0(x0)))))))))))))
2(1(0(0(0(0(2(0(0(0(2(0(x0)))))))))))) → 1(2(1(2(2(0(2(2(1(2(1(1(0(1(1(x0)))))))))))))))
2(0(2(0(1(2(2(0(2(1(0(0(0(x0))))))))))))) → 1(1(1(1(2(0(1(0(1(0(2(0(1(1(2(1(x0))))))))))))))))
2(2(2(2(0(0(1(2(2(1(1(0(0(x0))))))))))))) → 2(2(2(0(0(2(0(1(1(0(1(1(1(1(1(x0)))))))))))))))
0(0(1(0(1(1(1(0(1(0(2(0(0(1(x0)))))))))))))) → 1(2(1(1(1(1(0(1(1(0(0(2(1(0(0(0(x0))))))))))))))))
0(2(2(1(0(1(0(2(1(2(2(1(1(2(x0)))))))))))))) → 2(1(1(2(2(1(0(1(2(1(2(1(2(1(0(x0)))))))))))))))
0(2(2(0(1(0(0(2(2(2(1(2(2(2(2(x0))))))))))))))) → 2(2(1(0(2(1(2(2(0(0(0(1(0(0(1(1(x0))))))))))))))))
1(0(0(0(2(1(0(0(0(2(0(2(2(0(2(x0))))))))))))))) → 1(1(1(0(0(2(1(0(1(2(1(0(0(0(0(2(x0))))))))))))))))
1(0(1(2(0(1(1(0(2(1(0(2(0(1(0(x0))))))))))))))) → 1(0(0(1(1(1(2(1(0(2(0(1(0(1(1(1(0(x0)))))))))))))))))
0(2(1(0(0(1(0(2(2(0(0(2(0(0(2(1(x0)))))))))))))))) → 0(1(2(1(2(0(0(1(1(2(2(2(0(1(1(2(2(2(1(2(x0))))))))))))))))))))
2(0(2(0(2(2(0(2(0(1(0(0(0(0(1(2(x0)))))))))))))))) → 1(1(2(1(0(0(2(1(1(2(1(2(1(1(2(1(2(1(2(2(0(2(x0))))))))))))))))))))))
2(0(2(2(2(2(1(2(0(1(0(1(0(2(2(1(x0)))))))))))))))) → 2(1(2(1(2(2(2(0(0(1(2(2(1(0(0(2(x0))))))))))))))))
0(1(0(2(0(1(2(2(0(1(0(0(2(0(1(2(2(x0))))))))))))))))) → 1(2(2(1(2(1(2(2(1(0(0(0(0(0(0(0(2(x0)))))))))))))))))
0(1(0(2(2(0(2(2(0(2(1(0(2(1(0(0(2(x0))))))))))))))))) → 1(1(1(0(1(2(2(0(2(2(1(2(2(0(1(0(1(0(x0))))))))))))))))))
0(2(0(2(2(2(0(1(0(2(0(2(0(2(1(2(0(x0))))))))))))))))) → 1(0(1(1(0(2(2(0(1(2(1(0(0(1(2(1(0(1(x0))))))))))))))))))
1(1(0(1(0(2(1(0(2(0(1(2(2(2(2(1(1(x0))))))))))))))))) → 1(1(2(2(1(1(0(0(2(0(0(1(1(0(2(2(1(1(x0))))))))))))))))))
1(2(2(2(0(2(1(2(0(1(0(2(1(0(2(1(0(x0))))))))))))))))) → 1(1(1(2(1(0(1(1(2(2(0(1(2(1(2(1(0(0(2(1(2(1(2(x0)))))))))))))))))))))))
2(1(2(0(1(2(1(0(0(2(0(0(2(0(0(1(2(x0))))))))))))))))) → 1(2(1(2(1(1(2(0(2(0(2(1(1(1(1(0(2(1(1(x0)))))))))))))))))))
0(2(0(2(2(1(0(1(2(0(0(2(1(0(2(2(1(1(x0)))))))))))))))))) → 1(1(1(0(2(0(1(2(0(2(2(0(1(0(1(0(0(1(1(x0)))))))))))))))))))
0(2(2(2(0(1(0(2(0(1(0(0(0(2(2(2(2(0(x0)))))))))))))))))) → 2(1(2(1(2(0(0(0(2(0(0(1(1(0(2(1(2(0(0(2(x0))))))))))))))))))))
0(1(0(0(0(0(0(2(2(1(0(2(2(0(2(1(2(2(1(x0))))))))))))))))))) → 2(1(2(1(1(1(2(1(1(0(2(2(0(1(0(0(2(0(2(1(1(0(1(1(2(1(x0))))))))))))))))))))))))))
0(1(0(2(0(2(2(1(2(2(1(0(2(0(1(0(2(2(2(x0))))))))))))))))))) → 0(1(0(2(2(1(1(0(1(2(0(2(1(2(1(2(1(1(1(1(x0))))))))))))))))))))
1(0(1(1(2(0(1(1(0(0(2(1(0(0(2(2(0(0(0(x0))))))))))))))))))) → 2(1(1(0(1(1(2(1(2(2(2(2(1(1(1(1(2(1(1(2(0(0(2(1(x0))))))))))))))))))))))))
1(0(1(2(0(1(0(2(2(1(0(1(0(0(2(2(2(0(0(x0))))))))))))))))))) → 1(0(2(1(1(1(1(0(2(1(0(1(2(0(0(2(1(1(0(0(1(1(0(2(x0))))))))))))))))))))))))
1(2(0(2(2(0(0(1(0(0(2(0(2(2(1(0(1(0(2(x0))))))))))))))))))) → 2(2(1(2(1(0(2(1(2(2(1(2(2(0(2(2(0(2(0(0(1(1(1(x0)))))))))))))))))))))))
2(2(2(2(0(0(1(0(1(1(1(2(0(2(0(2(2(0(0(x0))))))))))))))))))) → 2(0(0(0(1(1(0(2(2(2(1(2(0(0(1(1(2(1(1(1(2(1(2(x0)))))))))))))))))))))))
0(0(1(0(0(0(2(2(1(0(2(1(2(1(2(2(2(0(0(2(x0)))))))))))))))))))) → 0(0(2(0(2(1(1(2(0(0(1(1(2(1(1(1(2(1(1(1(1(0(1(x0)))))))))))))))))))))))
0(1(2(1(0(1(0(2(2(2(2(1(0(2(1(0(1(1(1(1(x0)))))))))))))))))))) → 0(1(1(1(1(0(1(1(2(0(0(2(2(0(1(2(1(1(2(2(x0))))))))))))))))))))
1(1(0(0(1(2(1(0(0(1(1(2(1(0(0(0(1(2(1(2(x0)))))))))))))))))))) → 2(2(1(2(1(2(1(0(0(1(1(1(2(1(1(1(1(1(1(1(1(2(1(x0)))))))))))))))))))))))
1(1(0(2(2(0(0(0(2(1(2(1(0(1(0(0(0(0(0(1(x0)))))))))))))))))))) → 1(2(1(1(2(1(0(0(1(2(1(2(1(2(2(2(1(0(2(1(0(0(x0))))))))))))))))))))))
0(0(1(2(2(2(1(2(2(0(0(0(2(1(2(1(2(1(2(2(2(x0))))))))))))))))))))) → 1(1(2(1(1(1(1(2(1(1(0(2(1(0(0(2(1(2(1(2(1(0(0(x0)))))))))))))))))))))))
0(0(2(2(0(1(2(0(0(0(1(2(2(2(0(0(1(1(0(2(0(x0))))))))))))))))))))) → 1(2(1(0(1(1(1(2(1(2(0(2(1(1(2(0(2(2(1(2(0(0(1(1(0(2(x0))))))))))))))))))))))))))
0(2(2(0(1(0(0(0(2(2(1(0(1(2(0(1(0(1(0(0(0(x0))))))))))))))))))))) → 0(0(2(1(1(2(1(0(2(0(1(2(1(0(2(1(1(2(2(0(0(1(0(2(x0))))))))))))))))))))))))
0(2(2(0(1(2(2(2(2(1(2(0(2(1(0(1(0(2(0(1(2(x0))))))))))))))))))))) → 0(2(0(0(2(1(1(0(1(1(1(0(2(2(2(1(1(1(1(2(0(0(0(x0)))))))))))))))))))))))
1(0(0(0(1(2(1(2(0(2(0(0(1(0(0(0(1(2(1(0(2(x0))))))))))))))))))))) → 2(2(2(2(1(1(2(1(0(1(0(2(2(1(0(0(1(1(1(1(0(1(0(x0)))))))))))))))))))))))
1(0(2(1(1(1(1(0(0(2(2(0(1(0(1(0(2(2(0(0(0(x0))))))))))))))))))))) → 1(1(1(1(0(2(1(2(2(1(1(1(0(2(2(1(2(2(1(0(1(2(x0))))))))))))))))))))))
2(0(0(2(2(2(1(1(2(2(0(2(1(0(0(0(2(2(1(0(1(x0))))))))))))))))))))) → 2(1(1(2(1(1(1(0(1(2(2(1(2(0(0(0(2(0(0(1(2(0(x0))))))))))))))))))))))
2(0(2(2(2(0(0(1(2(2(1(1(2(0(0(0(2(0(0(0(2(x0))))))))))))))))))))) → 1(1(1(0(1(2(2(1(2(2(2(1(1(1(1(1(1(1(0(2(1(0(1(0(x0))))))))))))))))))))))))
2(1(2(1(1(2(0(0(1(1(0(1(1(2(1(1(1(1(0(1(2(x0))))))))))))))))))))) → 1(1(1(1(2(1(0(1(0(1(2(2(1(2(1(1(1(0(0(1(2(x0)))))))))))))))))))))
2(2(0(0(2(1(0(1(0(0(0(0(0(1(0(0(2(0(0(1(1(x0))))))))))))))))))))) → 2(0(2(0(2(0(0(0(2(2(1(1(2(2(2(1(1(1(1(1(2(1(2(x0)))))))))))))))))))))))
2(2(0(2(1(1(0(1(2(0(1(1(2(0(2(0(1(0(2(0(1(x0))))))))))))))))))))) → 2(1(2(1(0(1(1(1(1(0(2(2(2(1(2(2(1(2(1(1(0(2(x0))))))))))))))))))))))
0(0(1(2(2(0(1(1(2(0(1(0(0(0(0(1(0(1(2(2(2(1(x0)))))))))))))))))))))) → 1(1(1(1(2(2(2(0(2(0(2(2(1(0(2(0(2(1(2(1(2(1(1(1(0(1(x0))))))))))))))))))))))))))
1(0(1(1(0(0(1(1(1(0(2(2(0(1(0(0(1(2(0(0(2(0(x0)))))))))))))))))))))) → 1(1(1(2(2(0(2(1(2(0(2(0(0(0(1(2(1(2(1(2(0(2(1(x0)))))))))))))))))))))))
2(0(0(1(1(2(2(2(2(1(2(0(1(2(0(2(2(1(2(2(0(2(x0)))))))))))))))))))))) → 1(1(1(0(0(2(2(2(1(2(2(0(1(1(1(1(2(1(0(1(1(2(0(2(2(x0)))))))))))))))))))))))))
2(0(1(2(2(0(1(0(0(0(2(1(2(1(2(0(1(1(2(0(1(0(x0)))))))))))))))))))))) → 0(2(1(1(0(2(1(1(0(1(1(2(2(0(1(2(2(1(0(1(1(1(0(x0)))))))))))))))))))))))
2(2(1(0(1(1(2(0(2(1(1(0(0(1(2(1(2(2(2(0(2(1(x0)))))))))))))))))))))) → 2(1(1(2(1(2(0(2(1(1(1(1(2(1(1(2(1(1(0(1(1(2(2(1(1(x0)))))))))))))))))))))))))
2(2(2(0(0(1(0(2(0(2(0(0(1(2(1(2(1(2(0(1(1(1(x0)))))))))))))))))))))) → 1(1(2(1(2(1(2(1(2(1(0(2(0(1(1(0(1(0(0(2(0(2(1(2(1(x0)))))))))))))))))))))))))
0(0(1(2(0(0(1(0(0(2(0(1(0(1(2(0(2(0(0(2(2(0(2(x0))))))))))))))))))))))) → 0(0(1(0(1(2(2(0(1(0(0(2(0(1(1(1(0(1(2(1(2(0(0(1(0(1(x0))))))))))))))))))))))))))
2(2(1(2(0(0(0(0(1(2(1(0(1(0(2(0(1(0(0(1(2(0(2(x0))))))))))))))))))))))) → 2(1(1(2(2(2(2(1(0(1(2(0(1(1(1(1(1(2(1(2(1(1(0(2(1(1(0(0(2(x0)))))))))))))))))))))))))))))
1(2(0(2(1(2(0(0(0(0(0(0(2(2(1(0(2(2(0(2(1(0(0(1(x0)))))))))))))))))))))))) → 1(0(1(0(0(2(2(1(1(2(0(2(2(0(0(2(0(1(0(1(1(1(1(2(2(2(1(x0)))))))))))))))))))))))))))
1(2(2(1(2(0(1(2(0(1(2(1(0(0(0(2(2(2(0(2(2(0(2(1(x0)))))))))))))))))))))))) → 2(1(0(2(0(2(1(1(1(1(2(0(0(1(0(2(1(0(2(0(2(0(1(1(2(x0)))))))))))))))))))))))))
2(1(1(2(0(0(0(2(0(2(2(2(2(0(1(0(1(0(2(2(1(1(1(2(x0)))))))))))))))))))))))) → 2(1(1(2(1(1(2(1(2(1(2(0(1(1(0(0(0(1(1(1(2(1(2(1(1(x0)))))))))))))))))))))))))
0(1(0(1(1(0(1(1(0(2(2(0(2(1(0(0(2(0(0(1(2(0(2(0(2(x0))))))))))))))))))))))))) → 1(1(2(1(1(1(1(2(0(2(0(2(1(2(2(0(1(1(2(0(1(1(0(2(2(2(0(x0)))))))))))))))))))))))))))
0(1(2(2(1(0(0(2(1(1(2(0(1(0(2(0(1(0(1(2(2(0(1(1(0(x0))))))))))))))))))))))))) → 0(1(1(1(2(1(1(2(2(0(0(0(0(1(1(2(0(0(0(2(1(2(1(1(0(1(x0))))))))))))))))))))))))))
1(0(1(0(0(0(2(0(1(2(0(2(0(2(0(1(0(2(2(0(0(1(0(1(1(x0))))))))))))))))))))))))) → 1(2(0(0(2(0(1(0(1(0(2(2(1(1(0(0(0(1(2(1(1(1(1(0(2(1(x0))))))))))))))))))))))))))
1(1(0(2(0(1(2(1(0(0(1(0(0(2(1(0(2(0(1(0(0(0(1(0(1(x0))))))))))))))))))))))))) → 2(1(0(2(0(0(1(1(2(2(1(2(0(2(2(1(2(1(2(2(1(0(2(1(2(1(x0))))))))))))))))))))))))))
0(0(0(1(0(2(1(2(0(1(2(0(0(2(1(0(2(0(2(2(2(2(0(2(0(0(x0)))))))))))))))))))))))))) → 0(2(1(0(0(1(0(1(0(0(1(0(1(0(0(2(2(0(1(1(1(1(1(0(1(1(0(2(0(x0)))))))))))))))))))))))))))))
0(0(1(2(2(0(1(2(0(0(0(2(0(2(1(2(0(0(0(2(0(2(2(2(0(1(x0)))))))))))))))))))))))))) → 1(1(0(1(2(1(2(1(1(1(0(0(1(1(2(2(0(2(0(0(2(0(0(1(1(2(1(x0)))))))))))))))))))))))))))
0(2(0(2(2(2(0(1(1(2(2(2(0(0(1(2(0(2(2(1(2(0(0(1(2(2(x0)))))))))))))))))))))))))) → 0(1(1(2(1(0(2(1(1(1(1(2(1(1(1(2(1(1(2(0(2(0(2(2(1(2(1(2(0(x0)))))))))))))))))))))))))))))
2(1(2(2(0(0(2(0(0(0(1(1(2(0(1(1(2(2(2(0(0(0(2(1(2(1(x0)))))))))))))))))))))))))) → 1(1(0(0(0(1(1(0(2(0(1(2(1(1(1(1(2(1(1(1(1(2(1(0(1(2(2(1(x0))))))))))))))))))))))))))))
2(2(0(2(1(2(0(2(0(2(0(0(0(2(1(2(2(0(1(0(1(0(1(0(1(0(x0)))))))))))))))))))))))))) → 1(1(0(1(2(1(0(2(2(2(0(1(2(1(1(1(2(2(2(2(1(2(2(1(0(2(2(2(0(x0)))))))))))))))))))))))))))))
2(2(2(0(0(1(0(1(2(0(0(0(2(0(2(2(0(1(0(0(2(1(2(2(2(2(x0)))))))))))))))))))))))))) → 2(1(2(1(0(1(2(0(1(0(2(2(0(1(1(2(0(1(2(2(2(2(0(0(0(1(2(x0)))))))))))))))))))))))))))
2(2(2(2(0(1(1(2(0(2(0(1(1(2(0(1(2(1(1(2(2(1(2(1(2(2(x0)))))))))))))))))))))))))) → 2(0(0(1(1(2(2(1(1(1(1(0(1(2(1(2(1(1(2(1(2(2(1(0(2(1(1(0(2(x0)))))))))))))))))))))))))))))
0(1(0(0(2(0(0(2(2(2(0(1(2(1(1(1(2(0(1(1(0(0(0(1(0(1(0(x0))))))))))))))))))))))))))) → 0(1(0(0(1(0(1(2(0(2(0(0(2(0(1(2(2(1(1(1(0(1(2(1(0(0(0(x0)))))))))))))))))))))))))))
0(1(1(2(0(0(2(2(0(0(1(2(2(2(1(2(2(2(2(0(2(0(2(0(0(0(1(x0))))))))))))))))))))))))))) → 0(1(0(1(1(2(0(1(0(1(1(1(0(2(2(0(1(1(0(0(0(2(0(1(1(1(0(0(x0))))))))))))))))))))))))))))
1(0(1(1(1(2(2(1(0(1(0(2(1(1(0(2(1(0(1(2(1(0(2(2(1(0(0(x0))))))))))))))))))))))))))) → 2(2(2(2(1(2(1(1(1(2(2(2(1(2(2(2(1(1(0(1(1(2(1(0(2(2(1(1(x0))))))))))))))))))))))))))))
2(0(2(0(1(2(0(1(0(2(2(2(0(1(1(0(0(1(1(2(2(2(1(0(1(2(1(x0))))))))))))))))))))))))))) → 2(1(0(1(1(1(1(2(1(2(0(2(0(1(2(2(0(2(1(2(1(1(2(0(2(2(1(0(x0))))))))))))))))))))))))))))
2(2(2(0(2(1(2(2(1(0(1(1(1(0(1(2(1(1(2(1(2(0(1(0(2(2(1(x0))))))))))))))))))))))))))) → 0(1(0(1(2(1(2(2(1(2(1(2(1(0(2(1(2(2(1(1(2(1(1(0(2(0(2(x0)))))))))))))))))))))))))))
0(0(0(0(0(1(0(2(2(2(0(0(2(0(1(0(1(2(1(1(0(1(0(2(0(0(1(0(x0)))))))))))))))))))))))))))) → 1(0(2(1(2(1(2(1(1(2(1(1(1(1(1(1(1(1(0(2(2(1(2(1(1(1(0(1(0(1(x0))))))))))))))))))))))))))))))
1(2(2(1(1(2(2(1(1(2(1(2(2(0(0(1(2(1(0(1(1(0(1(0(0(2(2(0(x0)))))))))))))))))))))))))))) → 1(2(1(2(1(0(1(2(2(2(1(2(0(0(0(2(1(0(0(1(1(1(0(0(1(1(1(1(1(0(x0))))))))))))))))))))))))))))))
2(0(1(1(1(0(0(0(0(2(0(1(2(0(1(0(1(2(2(0(2(2(2(0(2(1(0(0(x0)))))))))))))))))))))))))))) → 1(1(0(1(1(2(2(1(2(1(0(2(0(0(2(1(1(1(1(2(0(1(0(1(1(1(1(2(1(1(x0))))))))))))))))))))))))))))))
2(2(2(2(2(1(0(2(2(0(2(1(0(0(1(1(2(1(1(1(1(2(2(0(0(2(2(0(x0)))))))))))))))))))))))))))) → 2(1(1(0(1(1(2(2(2(2(2(1(1(1(0(2(1(0(1(1(0(2(2(1(0(2(1(1(1(2(x0))))))))))))))))))))))))))))))
0(0(1(1(2(2(0(1(1(0(1(2(2(0(2(0(2(1(0(0(1(1(0(1(0(0(0(1(1(x0))))))))))))))))))))))))))))) → 0(1(2(0(1(1(0(1(1(0(2(1(2(1(1(0(2(1(1(2(2(1(1(2(1(2(2(2(0(2(x0))))))))))))))))))))))))))))))
0(2(2(1(0(1(2(0(1(0(1(2(0(1(1(0(1(2(0(0(2(0(1(2(0(1(1(2(1(x0))))))))))))))))))))))))))))) → 0(1(2(1(2(1(2(2(2(1(1(0(0(1(2(2(2(2(2(2(2(1(0(0(0(1(2(0(0(1(x0))))))))))))))))))))))))))))))
2(1(1(2(1(1(1(0(2(1(1(2(1(1(2(2(1(1(2(0(1(0(1(2(0(1(0(0(1(x0))))))))))))))))))))))))))))) → 2(2(1(1(1(0(1(2(1(0(1(2(1(1(1(2(1(0(2(0(1(2(1(0(0(1(1(2(1(x0)))))))))))))))))))))))))))))