Certification Problem

Input (TPDB TRS_Outermost/Strategy_outermost_added_08/n005)

The rewrite relation of the following TRS is considered.

f(x) → f(f(x)) (1)
The evaluation strategy is outermost

Property / Task

Prove or disprove termination.

Answer / Result

No.

Proof (by AProVE @ termCOMP 2023)

1 Loop

The following loop proves nontermination.

t0 = f(x)
→ f(f(x))
= t1
where t1 = t0σ and σ = {x/f(x)}