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.