Certification Problem

Input (TPDB TRS_Innermost/AG01_innermost/#4.17)

The rewrite relation of the following TRS is considered.

f(g(x),s(0),y) f(g(s(0)),y,g(x)) (1)
g(s(x)) s(g(x)) (2)
g(0) 0 (3)
The evaluation strategy is innermost.

Property / Task

Prove or disprove termination.

Answer / Result

Yes.

Proof (by AProVE @ termCOMP 2023)

1 Dependency Pair Transformation

The following set of initial dependency pairs has been identified.
f#(g(x),s(0),y) f#(g(s(0)),y,g(x)) (4)
f#(g(x),s(0),y) g#(s(0)) (5)
g#(s(x)) g#(x) (6)

1.1 Dependency Graph Processor

The dependency pairs are split into 2 components.