NO Nontermination Proof

Nontermination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

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

Proof

1 Loop

The following loop proves nontermination.

t0 = c(a(c(c(c(b(b(b(a(c(c(b(b(b(c(x0)))))))))))))))
→1.1 c(a(a(b(b(b(b(b(a(c(c(b(b(b(c(x0)))))))))))))))
→1.1.1 c(a(a(c(c(c(b(b(a(c(c(b(b(b(c(x0)))))))))))))))
→1.1.1 c(a(a(a(b(b(b(b(a(c(c(b(b(b(c(x0)))))))))))))))
→1 c(c(c(b(b(b(b(b(a(c(c(b(b(b(c(x0)))))))))))))))
→1.1.1 c(c(c(c(c(c(b(b(a(c(c(b(b(b(c(x0)))))))))))))))
→1.1.1 c(c(c(a(b(b(b(b(a(c(c(b(b(b(c(x0)))))))))))))))
→1.1.1.1 c(c(c(a(c(c(c(b(a(c(c(b(b(b(c(x0)))))))))))))))
→1.1.1.1 c(c(c(a(a(b(b(b(a(c(c(b(b(b(c(x0)))))))))))))))
→1.1.1.1.1 c(c(c(a(a(c(c(c(a(c(c(b(b(b(c(x0)))))))))))))))
→1.1.1.1.1 c(c(c(a(a(a(b(b(a(c(c(b(b(b(c(x0)))))))))))))))
→1.1.1 c(c(c(c(c(b(b(b(a(c(c(b(b(b(c(x0)))))))))))))))
→1.1 c(c(a(b(b(b(b(b(a(c(c(b(b(b(c(x0)))))))))))))))
→1.1.1 c(c(a(c(c(c(b(b(a(c(c(b(b(b(c(x0)))))))))))))))
→1.1.1 c(c(a(a(b(b(b(b(a(c(c(b(b(b(c(x0)))))))))))))))
→1.1.1.1 c(c(a(a(c(c(c(b(a(c(c(b(b(b(c(x0)))))))))))))))
→1.1.1.1 c(c(a(a(a(b(b(b(a(c(c(b(b(b(c(x0)))))))))))))))
→1.1 c(c(c(c(b(b(b(b(a(c(c(b(b(b(c(x0)))))))))))))))
→1 c(a(b(b(b(b(b(b(a(c(c(b(b(b(c(x0)))))))))))))))
→1.1 c(a(c(c(c(b(b(b(a(c(c(b(b(b(c(x0)))))))))))))))
= t19
where t19 = t0σ and σ = {x0/x0}