Term Rewriting System R:
[f, x, xs]
app(app(map, f), nil) -> nil
app(app(map, f), app(app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs))
app(app(treemap, f), app(app(node, x), xs)) -> app(app(node, app(f, x)), app(app(map, app(treemap, f)), xs))

Termination of R to be shown. 



   R
     ↳Dependency Pair Analysis



R contains the following Dependency Pairs:

APP(app(map, f), app(app(cons, x), xs)) -> APP(app(cons, app(f, x)), app(app(map, f), xs))
APP(app(map, f), app(app(cons, x), xs)) -> APP(cons, app(f, x))
APP(app(map, f), app(app(cons, x), xs)) -> APP(f, x)
APP(app(map, f), app(app(cons, x), xs)) -> APP(app(map, f), xs)
APP(app(treemap, f), app(app(node, x), xs)) -> APP(app(node, app(f, x)), app(app(map, app(treemap, f)), xs))
APP(app(treemap, f), app(app(node, x), xs)) -> APP(node, app(f, x))
APP(app(treemap, f), app(app(node, x), xs)) -> APP(f, x)
APP(app(treemap, f), app(app(node, x), xs)) -> APP(app(map, app(treemap, f)), xs)
APP(app(treemap, f), app(app(node, x), xs)) -> APP(map, app(treemap, f))

Furthermore, R contains one SCC. 


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




The following remains to be proven:
Dependency Pairs:

APP(app(treemap, f), app(app(node, x), xs)) -> APP(app(map, app(treemap, f)), xs)
APP(app(treemap, f), app(app(node, x), xs)) -> APP(f, x)
APP(app(treemap, f), app(app(node, x), xs)) -> APP(app(node, app(f, x)), app(app(map, app(treemap, f)), xs))
APP(app(map, f), app(app(cons, x), xs)) -> APP(app(map, f), xs)
APP(app(map, f), app(app(cons, x), xs)) -> APP(f, x)
APP(app(map, f), app(app(cons, x), xs)) -> APP(app(cons, app(f, x)), app(app(map, f), xs))


Rules:


app(app(map, f), nil) -> nil
app(app(map, f), app(app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs))
app(app(treemap, f), app(app(node, x), xs)) -> app(app(node, app(f, x)), app(app(map, app(treemap, f)), xs))




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