Certification Problem

Input (TPDB TRS_Standard/Zantema_05/z02)

The rewrite relation of the following TRS is considered.

a(f,a(f,x)) a(x,g) (1)
a(x,g) a(f,a(g,a(f,x))) (2)

Property / Task

Prove or disprove termination.

Answer / Result

Yes.

Proof (by ttt2 @ termCOMP 2023)

1 Bounds

The given TRS is match-(raise)-bounded by 4. This is shown by the following automaton. The automaton is closed under rewriting as it is compatible.