Certification Problem

Input (TPDB TRS_Standard/SK90/4.41)

The rewrite relation of the following TRS is considered.

f(a,y) f(y,g(y)) (1)
g(a) b (2)
g(b) b (3)

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.