MAYBE Termination Proof

Termination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

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

Proof

1 Termination Assumption

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