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