MAYBE Termination Proof

Termination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

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

Proof

1 Termination Assumption

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