Term Rewriting System R:
[f, x]
app(app(apply, f), x) -> app(f, x)
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
↳Argument Filtering and Ordering
Dependency Pair:
APP(app(apply, f), x) -> APP(f, x)
Rule:
app(app(apply, f), x) -> app(f, x)
The following dependency pair can be strictly oriented:
APP(app(apply, f), x) -> APP(f, x)
There are no usable rules w.r.t. to the AFS that need to be oriented.
Used ordering: Homeomorphic Embedding Order with EMB
resulting in one new DP problem.
Used Argument Filtering System: APP(x1, x2) -> APP(x1, x2)
app(x1, x2) -> app(x1, x2)
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳Dependency Graph
Dependency Pair:
Rule:
app(app(apply, f), x) -> app(f, x)
Using the Dependency Graph resulted in no new DP problems.
Termination of R successfully shown.
Duration:
0:00 minutes