Term Rewriting System R:
[x]
ap(ap(ff, x), x) -> ap(ap(x, ap(ff, x)), ap(ap(cons, x), nil))

Termination of R to be shown. 



   R
     ↳Dependency Pair Analysis



R contains the following Dependency Pairs:

AP(ap(ff, x), x) -> AP(ap(x, ap(ff, x)), ap(ap(cons, x), nil))
AP(ap(ff, x), x) -> AP(x, ap(ff, x))
AP(ap(ff, x), x) -> AP(ap(cons, x), nil)
AP(ap(ff, x), x) -> AP(cons, x)

Furthermore, R contains one SCC. 


   R
     ↳DPs
       →DP Problem 1
         ↳Remaining Obligation(s)




The following remains to be proven:
Dependency Pairs:

AP(ap(ff, x), x) -> AP(ap(cons, x), nil)
AP(ap(ff, x), x) -> AP(x, ap(ff, x))
AP(ap(ff, x), x) -> AP(ap(x, ap(ff, x)), ap(ap(cons, x), nil))


Rule:


ap(ap(ff, x), x) -> ap(ap(x, ap(ff, x)), ap(ap(cons, x), nil))




Termination of R could not be shown.
Duration:
0:00 minutes