NO Nontermination Proof

Nontermination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

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

Proof

1 Loop

The following loop proves nontermination.

t0 = a(a(a(b(a(a(x651))))))
→ε b(a(b(b(a(a(x651))))))
→ε a(b(a(b(a(a(x651))))))
→1 a(a(b(a(a(a(x651))))))
→1.1.1 a(a(b(b(a(b(x651))))))
→1.1.1 a(a(b(a(b(a(x651))))))
→1.1 a(a(a(b(a(a(x651))))))
= t6
where t6 = t0σ and σ = {x651/x651}