MAYBE Termination Proof

Termination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

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

Proof

1 Termination Assumption

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