Certification Problem

Input (TPDB TRS_Standard/Waldmann_06/jwttt)

The rewrite relation of the following TRS is considered.

f(x,f(a,y)) f(a,f(f(a,h(f(a,x))),y)) (1)

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#(x,f(a,y)) f#(a,f(f(a,h(f(a,x))),y)) (2)
f#(x,f(a,y)) f#(f(a,h(f(a,x))),y) (3)
f#(x,f(a,y)) f#(a,h(f(a,x))) (4)
f#(x,f(a,y)) f#(a,x) (5)

1.1 Dependency Graph Processor

The dependency pairs are split into 1 component.