MAYBE Termination Proof

Termination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

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

Proof

1 Termination Assumption

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