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

Innermost 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
         ↳Argument Filtering and 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)


Strategy:

innermost




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)


The following usable rule for innermost can be oriented:

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


Used ordering: Homeomorphic Embedding Order with EMB
resulting in one new DP problem.
Used Argument Filtering System:
APP(x1, x2) -> x1
app(x1, x2) -> app(x1, x2)


   R
     ↳DPs
       →DP Problem 1
         ↳AFS
           →DP Problem 2
             ↳Dependency Graph


Dependency Pair:


Rule:


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


Strategy:

innermost




Using the Dependency Graph resulted in no new DP problems.

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