Certification Problem

Input

The rewrite relation of the following TRS is considered.

id(x) x (1)
minus(x,0) x (2)
minus(s(x),s(y)) minus(x,y) (3)
div(0,s(y)) 0 (4)
div(s(x),s(y)) s(div(minus(x,y),id(s(y)))) (5)

Property / Task

Prove or disprove termination.

Answer / Result

Yes.

Proof (by unspecified)

1 Dependency Pair Transformation

The following set of initial dependency pairs has been identified.
div#(s(x),s(y)) div#(minus(x,y),id(s(y))) (6)
div#(s(x),s(y)) minus#(x,y) (7)
div#(s(x),s(y)) id#(s(y)) (8)
minus#(s(x),s(y)) minus#(x,y) (9)

1.1 Dependency Graph Processor

The dependency pairs are split into 2 components.