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