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