Certification Problem

Input (TPDB TRS_Standard/SK90/4.33)

The rewrite relation of the following TRS is considered.

a(b(a(x)))

→

b(a(b(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.

a^#(b(a(x)))

→

a^#(b(x))

(2)

1.1 Dependency Graph Processor

The dependency pairs are split into 1 component.

The 1^st component contains the pair
a^#(b(a(x))) → a^#(b(x)) (2)

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

[a(x₁)] = x₁ + 1

[b(x₁)] = x₁ + 28958

[a^#(x₁)] = x₁ + 0

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

The dependency pairs are split into 0 components.