Certification Problem

Input (TPDB TRS_Standard/Applicative_05/Ex6_11)

The rewrite relation of the following TRS is considered.

app(app(F,app(app(F,f),x)),x) app(app(F,app(G,app(app(F,f),x))),app(f,x)) (1)

Property / Task

Prove or disprove termination.

Answer / Result

Yes.

Proof (by ttt2 @ termCOMP 2023)

1 Dependency Pair Transformation

The following set of initial dependency pairs has been identified.
app#(app(F,app(app(F,f),x)),x) app#(f,x) (2)
app#(app(F,app(app(F,f),x)),x) app#(G,app(app(F,f),x)) (3)
app#(app(F,app(app(F,f),x)),x) app#(F,app(G,app(app(F,f),x))) (4)
app#(app(F,app(app(F,f),x)),x) app#(app(F,app(G,app(app(F,f),x))),app(f,x)) (5)

1.1 Dependency Graph Processor

The dependency pairs are split into 1 component.