Certification Problem

Input (TPDB TRS_Standard/AotoYamada_05/025)

The rewrite relation of the following TRS is considered.

app(app(apply,f),x)

→

app(f,x)

(1)

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.

app^#(app(apply,f),x)

→

app^#(f,x)

(2)

1.1 Dependency Graph Processor

The dependency pairs are split into 1 component.

The 1^st component contains the pair
app^#(app(apply,f),x) → app^#(f,x) (2)

1.1.1 Reduction Pair Processor with Usable Rules
Using the Max-polynomial interpretation

[apply] = 1

[app^#(x₁, x₂)] = x₁ + 0

[app(x₁, x₂)] = x₁ + x₂ + 0

having no usable rules (w.r.t. the implicit argument filter of the reduction pair), the pair
app^#(app(apply,f),x) → app^#(f,x) (2)
could be deleted.
1.1.1.1 Dependency Graph Processor

The dependency pairs are split into 0 components.