MAYBE Termination Proof

Termination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

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

Proof

1 Termination Assumption

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