Certification Problem

Input (TPDB TRS_Standard/AG01/#3.7)

The rewrite relation of the following TRS is considered.

half(0) 0 (1)
half(s(s(x))) s(half(x)) (2)
log(s(0)) 0 (3)
log(s(s(x))) s(log(s(half(x)))) (4)

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.
log#(s(s(x))) log#(s(half(x))) (5)
log#(s(s(x))) half#(x) (6)
half#(s(s(x))) half#(x) (7)

1.1 Dependency Graph Processor

The dependency pairs are split into 2 components.