Certification Problem

Input (TPDB TRS_Standard/AProVE_04/forward_instantiation2)

The rewrite relation of the following TRS is considered.

f(x,y,z) g(x,y,z) (1)
g(0,1,x) f(x,x,x) (2)
a b (3)
a c (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 3. This is shown by the following automaton. The automaton is closed under rewriting as it is compatible.