NO Nontermination Proof

Nontermination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

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

Proof

1 Loop

The following loop proves nontermination.

t0 = a(a(a(b(a(a(x2855))))))
→ε b(b(b(b(a(a(x2855))))))
→ε a(b(a(b(b(a(a(x2855)))))))
→1.1.1 a(b(a(a(b(a(a(a(x2855))))))))
→1.1.1.1.1 a(b(a(a(b(b(b(b(x2855))))))))
→1.1.1.1 a(b(a(a(a(b(a(b(b(x2855)))))))))
→1.1.1.1.1.1.1 a(b(a(a(a(b(a(a(b(a(x2855))))))))))
= t6
where t6 = C[t0σ] and σ = {x2855/b(a(x2855))} and C = a(b(☐))