MAYBE Termination Proof

Termination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

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

Proof

1 Termination Assumption

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