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

Proof

1 Loop

The following loop proves nontermination.

t0 = a(b(b(b(c(b(b(x70155)))))))
→ε b(b(c(a(b(b(c(b(b(x70155)))))))))
→1.1.1 b(b(c(b(b(c(a(b(c(b(b(x70155)))))))))))
→1.1.1 b(b(c(b(c(a(b(c(b(b(x70155))))))))))
→1.1.1 b(b(c(c(a(b(c(b(b(x70155)))))))))
→1 b(a(a(b(c(b(b(x70155)))))))
→1.1 b(a(b(b(c(a(c(b(b(x70155)))))))))
→1.1.1.1.1 b(a(b(b(c(c(b(b(x70155))))))))
→1.1.1 b(a(b(a(b(b(x70155))))))
→1.1.1 b(a(b(b(b(c(a(b(x70155))))))))
→1.1.1.1.1.1 b(a(b(b(b(c(b(b(c(a(x70155))))))))))
= t10
where t10 = C[t0σ] and σ = {x70155/c(a(x70155))} and C = b(☐)