Certification Problem

Input (TPDB TRS_Standard/Der95/09)

The rewrite relation of the following TRS is considered.

.(.(x,y),z)

→

.(x,.(y,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)	→	.^#(y,z)	(2)
.^#(.(x,y),z)	→	.^#(x,.(y,z))	(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,z)) (3)

.^#(.(x,y),z) → .^#(y,z) (2)

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

[.^#(x₁, x₂)] = x₁ + 0

[.(x₁, x₂)] = x₁ + x₂ + 1

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

.^#(.(x,y),z) → .^#(x,.(y,z)) (3)

.^#(.(x,y),z) → .^#(y,z) (2)

could be deleted.
1.1.1.1 Dependency Graph Processor

The dependency pairs are split into 0 components.