Certification Problem

Input (TPDB TRS_Standard/Zantema_05/jw11)

The rewrite relation of the following TRS is considered.

f(a,f(x,a)) f(a,f(f(a,x),f(a,a))) (1)

Property / Task

Prove or disprove termination.

Answer / Result

Yes.

Proof (by ttt2 @ termCOMP 2023)

1 Bounds

The given TRS is match-(raise)-bounded by 1. This is shown by the following automaton. The automaton is closed under rewriting as it is compatible.