Certification Problem

Input (TPDB TRS_Standard/AProVE_04/improved_usable2)

The rewrite relation of the following TRS is considered.

f(a,x) f(g(x),x) (1)
h(g(x)) h(a) (2)
g(h(x)) g(x) (3)
h(h(x)) x (4)

Property / Task

Prove or disprove termination.

Answer / Result

Yes.

Proof (by ttt2 @ termCOMP 2023)

1 Bounds

The given TRS is roof-(raise)-bounded by 2. This is shown by the following automaton. The automaton is closed under rewriting as it is compatible.