Certification Problem

Input (TPDB TRS_Standard/AG01/#3.53b)

The rewrite relation of the following TRS is considered.

g(x,y) x (1)
g(x,y) y (2)
f(0,1,x) f(s(x),x,x) (3)
f(x,y,s(z)) s(f(0,1,z)) (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.
f#(x,y,s(z)) f#(0,1,z) (5)
f#(0,1,x) f#(s(x),x,x) (6)

1.1 Dependency Graph Processor

The dependency pairs are split into 1 component.