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

Proof

1 Loop

The following loop proves nontermination.

t0 = a(b(b(x10285)))
→ε a(c(b(b(a(a(b(x10285)))))))
→1.1 a(c(b(a(a(b(x10285))))))
→1.1 a(c(a(a(b(x10285)))))
→1.1 a(c(a(b(x10285))))
→1.1 a(c(a(c(b(b(a(a(x10285))))))))
→1.1 a(c(c(b(b(a(a(x10285)))))))
→1 a(b(b(a(a(x10285)))))
= t7
where t7 = t0σ and σ = {x10285/a(a(x10285))}