NO Nontermination Proof

Nontermination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

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

Proof

1 Loop

The following loop proves nontermination.

t0 = a(b(c(x9865)))
→ε b(a(a(c(a(a(c(x9865)))))))
→1.1.1.1 b(a(a(c(a(c(x9865))))))
→1.1.1.1 b(a(a(c(c(x9865)))))
→1.1.1 b(a(a(b(x9865))))
→1.1 b(a(b(a(a(c(a(a(x9865))))))))
→1.1.1 b(a(b(a(c(a(a(x9865)))))))
→1.1.1 b(a(b(c(a(a(x9865))))))
= t7
where t7 = C[t0σ] and σ = {x9865/a(a(x9865))} and C = b(☐)