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