Certification Problem

Input (TPDB TRS_Standard/Der95/18)

The rewrite relation of the following TRS is considered.

*(x,+(y,z))

→

+(*(x,y),*(x,z))

(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.

*^#(x,+(y,z))	→	*^#(x,z)	(2)
*^#(x,+(y,z))	→	*^#(x,y)	(3)

1.1 Dependency Graph Processor

The dependency pairs are split into 1 component.

The 1^st component contains the pair

*^#(x,+(y,z)) → *^#(x,y) (3)

*^#(x,+(y,z)) → *^#(x,z) (2)

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

[*^#(x₁, x₂)] = x₂ + 0

[+(x₁, x₂)] = x₁ + x₂ + 1

[*(x₁, x₂)] = 0

having no usable rules (w.r.t. the implicit argument filter of the reduction pair), the pairs

*^#(x,+(y,z)) → *^#(x,y) (3)

*^#(x,+(y,z)) → *^#(x,z) (2)

could be deleted.
1.1.1.1 Dependency Graph Processor

The dependency pairs are split into 0 components.