Certification Problem

Input (TPDB TRS_Standard/SK90/4.55)

The rewrite relation of the following TRS is considered.

f(x,x) f(a,b) (1)
b c (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 2. This is shown by the following automaton. The automaton is closed under rewriting as it is state-compatible w.r.t. the following relation.
2 » 2
4 » 8
4 » 4
1 » 1
3 » 8
3 » 3
8 » 8