Term Rewriting System R:
[y]
f(a, y) -> f(y, g(y))
g(a) -> b
g(b) -> b
Innermost Termination of R to be shown.
R
↳Dependency Pair Analysis
R contains the following Dependency Pairs:
F(a, y) -> F(y, g(y))
F(a, y) -> G(y)
Furthermore, R contains one SCC.
R
↳DPs
→DP Problem 1
↳Polynomial Ordering
Dependency Pair:
F(a, y) -> F(y, g(y))
Rules:
f(a, y) -> f(y, g(y))
g(a) -> b
g(b) -> b
Strategy:
innermost
The following dependency pair can be strictly oriented:
F(a, y) -> F(y, g(y))
Additionally, the following usable rules for innermost w.r.t. to the implicit AFS can be oriented:
g(a) -> b
g(b) -> b
Used ordering: Polynomial ordering with Polynomial interpretation:
| POL(g(x1)) | = 0 |
| POL(b) | = 0 |
| POL(a) | = 1 |
| POL(F(x1, x2)) | = x1 + x2 |
resulting in one new DP problem.
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Dependency Graph
Dependency Pair:
Rules:
f(a, y) -> f(y, g(y))
g(a) -> b
g(b) -> b
Strategy:
innermost
Using the Dependency Graph resulted in no new DP problems.
Innermost Termination of R successfully shown.
Duration:
0:00 minutes