Certification Problem

Input (TPDB TRS_Standard/AProVE_04/improved_usable2)

The rewrite relation of the following TRS is considered.

f(a,x) f(g(x),x) (1)
h(g(x)) h(a) (2)
g(h(x)) g(x) (3)
h(h(x)) x (4)

Property / Task

Prove or disprove termination.

Answer / Result

Yes.

Proof (by AProVE @ termCOMP 2023)

1 Dependency Pair Transformation

The following set of initial dependency pairs has been identified.
f#(a,x) f#(g(x),x) (5)
f#(a,x) g#(x) (6)
h#(g(x)) h#(a) (7)
g#(h(x)) g#(x) (8)

1.1 Dependency Graph Processor

The dependency pairs are split into 2 components.