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

Proof

1 Termination Assumption

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