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

Proof

1 Loop

The following loop proves nontermination.

t0 = a(b(b(x11064)))
→ε a(a(c(b(b(a(b(x11064)))))))
→1.1.1 a(a(c(b(a(b(x11064))))))
→1.1.1 a(a(c(a(b(x11064)))))
→1.1.1 a(a(c(a(a(c(b(b(a(x11064)))))))))
→1.1.1 a(a(c(a(c(b(b(a(x11064))))))))
→1.1.1 a(a(c(c(b(b(a(x11064)))))))
→1.1 a(a(b(b(a(x11064)))))
= t7
where t7 = C[t0σ] and σ = {x11064/a(x11064)} and C = a(☐)