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

Proof

1 Termination Assumption

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