NO Nontermination Proof

Nontermination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

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

Proof

1 Loop

The following loop proves nontermination.

t0 = b(b(b(b(a(a(a(a(b(x0)))))))))
→1.1.1.1 b(b(b(b(b(a(a(a(b(x0)))))))))
→ε a(a(b(b(b(b(a(a(a(b(x0))))))))))
→1.1 a(a(a(a(b(b(b(a(a(a(b(x0)))))))))))
→1.1.1.1 a(a(a(a(a(a(b(b(a(a(a(b(x0))))))))))))
→1.1.1.1.1.1 a(a(a(a(a(a(a(a(b(a(a(a(b(x0)))))))))))))
→ε b(a(a(a(a(a(a(a(b(a(a(a(b(x0)))))))))))))
→1 b(b(a(a(a(a(a(a(b(a(a(a(b(x0)))))))))))))
→1.1 b(b(b(a(a(a(a(a(b(a(a(a(b(x0)))))))))))))
→1.1.1 b(b(b(b(a(a(a(a(b(a(a(a(b(x0)))))))))))))
= t9
where t9 = t0σ and σ = {x0/a(a(a(b(x0))))}