MAYBE Termination Proof

Termination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

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

Proof

1 Termination Assumption

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