Certification Problem

Input (TPDB TRS_Standard/AG01/#3.29)

The rewrite relation of the following TRS is considered.

f(s(x),y,y)

→

f(y,x,s(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.

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

→

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

(2)

1.1 Dependency Graph Processor

The dependency pairs are split into 1 component.

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

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

[s(x₁)] = x₁ + 1

[f(x₁, x₂, x₃)] = 0

[f^#(x₁, x₂, x₃)] = x₁ + x₂ + 0

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

The dependency pairs are split into 0 components.