MAYBE Termination Proof

Termination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

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

Proof

1 Termination Assumption

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