Certification Problem

Input (TPDB SRS_Standard/Zantema_04/z063)

The rewrite relation of the following TRS is considered.

b(a(b(c(c(b(x1))))))

→

a(b(b(c(c(b(a(x1)))))))

(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.

b^#(a(b(c(c(b(x1))))))	→	b^#(c(c(b(a(x1)))))	(2)
b^#(a(b(c(c(b(x1))))))	→	b^#(a(x1))	(3)
b^#(a(b(c(c(b(x1))))))	→	b^#(b(c(c(b(a(x1))))))	(4)

1.1 Dependency Graph Processor

The dependency pairs are split into 1 component.

The 1^st component contains the pair
b^#(a(b(c(c(b(x1)))))) → b^#(a(x1)) (3)

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

[a(x₁)] = x₁ + 1

[b(x₁)] = x₁ + 1

[c(x₁)] = x₁ + 0

[b^#(x₁)] = x₁ + 0

having no usable rules (w.r.t. the implicit argument filter of the reduction pair), the pair
b^#(a(b(c(c(b(x1)))))) → b^#(a(x1)) (3)
could be deleted.
1.1.1.1 Dependency Graph Processor

The dependency pairs are split into 0 components.