Term Rewriting System R:
[x, y]
h(f(x), y) -> f(g(x, y))
g(x, y) -> h(x, y)
Termination of R to be shown.
R
↳Dependency Pair Analysis
R contains the following Dependency Pairs:
H(f(x), y) -> G(x, y)
G(x, y) -> H(x, y)
Furthermore, R contains one SCC.
R
↳DPs
→DP Problem 1
↳Polynomial Ordering
Dependency Pairs:
G(x, y) -> H(x, y)
H(f(x), y) -> G(x, y)
Rules:
h(f(x), y) -> f(g(x, y))
g(x, y) -> h(x, y)
The following dependency pair can be strictly oriented:
G(x, y) -> H(x, y)
There are no usable rules using the Ce-refinement that need to be oriented.
Used ordering: Polynomial ordering with Polynomial interpretation:
| POL(G(x1, x2)) | = 1 + x1 |
| POL(H(x1, x2)) | = x1 |
| POL(f(x1)) | = 1 + x1 |
resulting in one new DP problem.
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Dependency Graph
Dependency Pair:
H(f(x), y) -> G(x, y)
Rules:
h(f(x), y) -> f(g(x, y))
g(x, y) -> h(x, y)
Using the Dependency Graph resulted in no new DP problems.
Termination of R successfully shown.
Duration:
0:00 minutes