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

Proof

1 Termination Assumption

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