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 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