MAYBE Termination Proof

Termination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

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

Proof

1 Termination Assumption

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