Term Rewriting System R:
[]
f(0) -> cons(0)
f(s(0)) -> f(p(s(0)))
p(s(0)) -> 0
Termination of R to be shown.
R
↳Dependency Pair Analysis
R contains the following Dependency Pairs:
F(s(0)) -> F(p(s(0)))
F(s(0)) -> P(s(0))
Furthermore, R contains one SCC.
R
↳DPs
→DP Problem 1
↳Polynomial Ordering
Dependency Pair:
F(s(0)) -> F(p(s(0)))
Rules:
f(0) -> cons(0)
f(s(0)) -> f(p(s(0)))
p(s(0)) -> 0
The following dependency pair can be strictly oriented:
F(s(0)) -> F(p(s(0)))
Additionally, the following rules can be oriented:
f(0) -> cons(0)
f(s(0)) -> f(p(s(0)))
p(s(0)) -> 0
Used ordering: Polynomial ordering with Polynomial interpretation:
| POL(0) | = 0 |
| POL(cons(x1)) | = 0 |
| POL(s(x1)) | = 1 |
| POL(f(x1)) | = 0 |
| POL(F(x1)) | = x1 |
| POL(p(x1)) | = 0 |
resulting in one new DP problem.
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Dependency Graph
Dependency Pair:
Rules:
f(0) -> cons(0)
f(s(0)) -> f(p(s(0)))
p(s(0)) -> 0
Using the Dependency Graph resulted in no new DP problems.
Termination of R successfully shown.
Duration:
0:00 minutes