Term Rewriting System R:
[f, x, y]
app(app(app(uncurry, f), x), y) -> app(app(f, x), y)

Termination of R to be shown.

R
Dependency Pair Analysis

R contains the following Dependency Pairs:

APP(app(app(uncurry, f), x), y) -> APP(app(f, x), y)
APP(app(app(uncurry, f), x), y) -> APP(f, x)

Furthermore, R contains one SCC.

R
DPs
→DP Problem 1
Polynomial Ordering

Dependency Pairs:

APP(app(app(uncurry, f), x), y) -> APP(f, x)
APP(app(app(uncurry, f), x), y) -> APP(app(f, x), y)

Rule:

app(app(app(uncurry, f), x), y) -> app(app(f, x), y)

The following dependency pairs can be strictly oriented:

APP(app(app(uncurry, f), x), y) -> APP(f, x)
APP(app(app(uncurry, f), x), y) -> APP(app(f, x), y)

Additionally, the following usable rule w.r.t. to the implicit AFS can be oriented:

app(app(app(uncurry, f), x), y) -> app(app(f, x), y)

Used ordering: Polynomial ordering with Polynomial interpretation:
 POL(uncurry) =  1 POL(app(x1, x2)) =  x1 + x2 POL(APP(x1, x2)) =  1 + x1

resulting in one new DP problem.

R
DPs
→DP Problem 1
Polo
→DP Problem 2
Dependency Graph

Dependency Pair:

Rule:

app(app(app(uncurry, f), x), y) -> app(app(f, x), y)

Using the Dependency Graph resulted in no new DP problems.

Termination of R successfully shown.
Duration:
0:00 minutes