MAYBE Termination Proof

Termination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

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

Proof

1 Termination Assumption

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