Certification Problem

Input (TPDB TRS_Standard/Endrullis_06/pair3rotate)

The rewrite relation of the following TRS is considered.

p(a(x0),p(b(x1),p(a(x2),x3))) p(x2,p(a(a(x0)),p(b(x1),x3))) (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.
p#(a(x0),p(b(x1),p(a(x2),x3))) p#(a(a(x0)),p(b(x1),x3)) (2)
p#(a(x0),p(b(x1),p(a(x2),x3))) p#(b(x1),x3) (3)
p#(a(x0),p(b(x1),p(a(x2),x3))) p#(x2,p(a(a(x0)),p(b(x1),x3))) (4)

1.1 Dependency Graph Processor

The dependency pairs are split into 1 component.