Certification Problem

Input (TPDB TRS_Standard/AProVE_04/improved_usable)

The rewrite relation of the following TRS is considered.

f(a,h(x)) f(g(x),h(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 NaTT @ termCOMP 2023)

1 Dependency Pair Transformation

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

1.1 Dependency Graph Processor

The dependency pairs are split into 2 components.