Certification Problem

Input (TPDB TRS_Standard/Strategy_removed_mixed_05/n001)

The rewrite relation of the following TRS is considered.

h(f(f(x))) h(f(g(f(x)))) (1)
f(g(f(x))) f(f(x)) (2)

Property / Task

Prove or disprove termination.

Answer / Result

No.

Proof (by ttt2 @ termCOMP 2023)

1 Loop

The following loop proves nontermination.

t0 = h(f(f(x8)))
h(f(g(f(x8))))
h(f(f(x8)))
= t2
where t2 = t0σ and σ = {x8/x8}