Certification Problem

Input (TPDB TRS_Standard/HirokawaMiddeldorp_04/t006)

The rewrite relation of the following TRS is considered.

f(g(x,y),f(y,y))

→

f(g(y,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),f(y,y))

→

f^#(g(y,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),f(y,y)) → f^#(g(y,x),y) (2)

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

[f(x₁, x₂)] = x₁ + 1

[f^#(x₁, x₂)] = x₂ + 0

[g(x₁, x₂)] = 0

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

The dependency pairs are split into 0 components.