MAYBE Termination Proof

Termination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

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

Proof

1 Termination Assumption

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