Term Rewriting System R:
[x, f, t]
app(app(fmap, fnil), x) -> nil
app(app(fmap, app(app(fcons, f), t)), x) -> app(app(cons, app(f, x)), app(app(fmap, t), x))

Innermost Termination of R to be shown. 



   R
     ↳Dependency Pair Analysis



R contains the following Dependency Pairs:

APP(app(fmap, app(app(fcons, f), t)), x) -> APP(app(cons, app(f, x)), app(app(fmap, t), x))
APP(app(fmap, app(app(fcons, f), t)), x) -> APP(cons, app(f, x))
APP(app(fmap, app(app(fcons, f), t)), x) -> APP(f, x)
APP(app(fmap, app(app(fcons, f), t)), x) -> APP(app(fmap, t), x)
APP(app(fmap, app(app(fcons, f), t)), x) -> APP(fmap, t)

Furthermore, R contains one SCC. 


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




The following remains to be proven:
Dependency Pairs:

APP(app(fmap, app(app(fcons, f), t)), x) -> APP(app(fmap, t), x)
APP(app(fmap, app(app(fcons, f), t)), x) -> APP(f, x)
APP(app(fmap, app(app(fcons, f), t)), x) -> APP(app(cons, app(f, x)), app(app(fmap, t), x))


Rules:


app(app(fmap, fnil), x) -> nil
app(app(fmap, app(app(fcons, f), t)), x) -> app(app(cons, app(f, x)), app(app(fmap, t), x))


Strategy:

innermost



Innermost Termination of R could not be shown.
Duration:
0:02 minutes