MAYBE Termination Proof

Termination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

b(a(a(b(b(x0))))) → b(a(a(a(a(b(b(x0)))))))
b(a(b(b(x0)))) → b(b(x0))
b(a(b(a(a(a(a(b(x0)))))))) → b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))
b(a(a(b(a(a(a(a(b(x0))))))))) → b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))
b(a(a(a(b(a(a(a(a(b(x0)))))))))) → b(x0)

Proof

1 Termination Assumption

We assume termination of the following TRS
b(a(a(b(b(x0))))) → b(a(a(a(a(b(b(x0)))))))
b(a(b(b(x0)))) → b(b(x0))
b(a(b(a(a(a(a(b(x0)))))))) → b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))
b(a(a(b(a(a(a(a(b(x0))))))))) → b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))
b(a(a(a(b(a(a(a(a(b(x0)))))))))) → b(x0)