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

Proof

1 Termination Assumption

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