Certification Problem

Input (TPDB TRS_Standard/SK90/2.59)

The rewrite relation of the following TRS is considered.

f(g(x),y,y)

→

g(f(x,x,y))

(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.

f^#(g(x),y,y)

→

f^#(x,x,y)

(2)

1.1 Dependency Graph Processor

The dependency pairs are split into 1 component.

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

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

[f(x₁, x₂, x₃)] = 0

[f^#(x₁, x₂, x₃)] = x₁ + 0

[g(x₁)] = x₁ + 1

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

The dependency pairs are split into 0 components.