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)))) → a(c(a(c(c(x0)))))
c(c(c(x0))) → a(a(a(x0)))

Proof

1 Loop

The following loop proves nontermination.

t0 = a(a(a(a(c(a(a(a(c(a(a(c(a(x7473)))))))))))))
→ε a(c(a(c(c(c(a(a(a(c(a(a(c(a(x7473))))))))))))))
→1.1.1 a(c(a(a(a(a(a(a(a(c(a(a(c(a(x7473))))))))))))))
→1.1.1.1.1 a(c(a(a(a(a(c(a(c(c(c(a(a(c(a(x7473)))))))))))))))
→1.1.1.1.1.1.1.1 a(c(a(a(a(a(c(a(a(a(a(a(a(c(a(x7473)))))))))))))))
→1.1.1.1.1.1.1.1.1 a(c(a(a(a(a(c(a(a(a(c(a(c(c(c(a(x7473))))))))))))))))
→1.1.1.1.1.1.1.1.1.1.1.1 a(c(a(a(a(a(c(a(a(a(c(a(a(a(a(a(x7473))))))))))))))))
→1.1.1.1.1.1.1.1.1.1.1.1 a(c(a(a(a(a(c(a(a(a(c(a(a(c(a(c(c(x7473)))))))))))))))))
= t7
where t7 = C[t0σ] and σ = {x7473/c(c(x7473))} and C = a(c(☐))