MAYBE Termination Proof

Termination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

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

Proof

1 Termination Assumption

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