Certification Problem

Input (TPDB TRS_Standard/SK90/4.15)

The rewrite relation of the following TRS is considered.

+(-(x,y),z)	→	-(+(x,z),y)	(1)
-(+(x,y),y)	→	x	(2)

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)	(3)
+^#(-(x,y),z)	→	-^#(+(x,z),y)	(4)

1.1 Dependency Graph Processor

The dependency pairs are split into 1 component.

The 1^st component contains the pair
+^#(-(x,y),z) → +^#(x,z) (3)

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

[-(x₁, x₂)] = x₁ + 1

[-^#(x₁, x₂)] = 0

[+(x₁, x₂)] = 0

[+^#(x₁, x₂)] = x₁ + 0

having no usable rules (w.r.t. the implicit argument filter of the reduction pair), the pair
+^#(-(x,y),z) → +^#(x,z) (3)
could be deleted.
1.1.1.1 Dependency Graph Processor

The dependency pairs are split into 0 components.