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(c(b(a(a(x0))))))
c(b(c(x0))) → x0

Proof

1 Loop

The following loop proves nontermination.

t0 = a(b(b(c(b(x14133)))))
→ε b(a(c(b(a(a(b(c(b(x14133)))))))))
→1.1.1.1.1 b(a(c(b(a(b(a(c(b(a(a(c(b(x14133)))))))))))))
→1.1.1.1.1.1.1.1.1 b(a(c(b(a(b(a(c(b(a(c(b(x14133))))))))))))
→1.1.1.1.1.1.1.1.1 b(a(c(b(a(b(a(c(b(c(b(x14133)))))))))))
→1.1.1.1.1.1.1 b(a(c(b(a(b(a(b(x14133))))))))
→1.1.1.1.1.1 b(a(c(b(a(b(b(a(c(b(a(a(x14133))))))))))))
→1.1.1.1.1.1.1 b(a(c(b(a(b(b(c(b(a(a(x14133)))))))))))
= t7
where t7 = C[t0σ] and σ = {x14133/a(a(x14133))} and C = b(a(c(b(☐))))