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

Proof

1 Termination Assumption

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