Certification Problem

Input (TPDB TRS_Standard/AG01/#3.41)

The rewrite relation of the following TRS is considered.

p(s(x)) x (1)
fac(0) s(0) (2)
fac(s(x)) times(s(x),fac(p(s(x)))) (3)

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.
fac#(s(x)) p#(s(x)) (4)
fac#(s(x)) fac#(p(s(x))) (5)

1.1 Dependency Graph Processor

The dependency pairs are split into 1 component.