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
     ↳Overlay and local confluence Check



The TRS is overlay and locally confluent (all critical pairs are trivially joinable).Hence, we can switch to innermost. 


   R
     ↳OC
       →TRS2
         ↳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)

R contains no SCCs.

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