NO Nontermination Proof

Nontermination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

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

Proof

1 Loop

The following loop proves nontermination.

t0 = a(a(b(b(a(b(b(a(x664))))))))
→ε b(a(b(b(b(a(b(b(a(x664)))))))))
→1.1 b(a(a(a(a(b(b(a(x664))))))))
→1.1.1 b(a(a(b(a(b(b(b(a(x664)))))))))
→1.1.1.1.1 b(a(a(b(a(a(a(a(x664))))))))
→1.1.1.1 b(a(a(b(b(a(b(a(a(x664)))))))))
→1.1.1.1.1.1.1 b(a(a(b(b(a(b(b(a(b(x664))))))))))
= t6
where t6 = C[t0σ] and σ = {x664/b(x664)} and C = b(☐)