Term Rewriting System R:
[y, x, f, xs]
app(app(plus, 0), y) -> y
app(app(plus, app(s, x)), y) -> app(s, app(app(plus, x), y))
app(app(sumwith, f), nil) -> nil
app(app(sumwith, f), app(app(cons, x), xs)) -> app(app(plus, app(f, x)), app(app(sumwith, f), xs))

Termination of R to be shown.

R
Dependency Pair Analysis

R contains the following Dependency Pairs:

APP(app(plus, app(s, x)), y) -> APP(s, app(app(plus, x), y))
APP(app(plus, app(s, x)), y) -> APP(app(plus, x), y)
APP(app(plus, app(s, x)), y) -> APP(plus, x)
APP(app(sumwith, f), app(app(cons, x), xs)) -> APP(app(plus, app(f, x)), app(app(sumwith, f), xs))
APP(app(sumwith, f), app(app(cons, x), xs)) -> APP(plus, app(f, x))
APP(app(sumwith, f), app(app(cons, x), xs)) -> APP(f, x)
APP(app(sumwith, f), app(app(cons, x), xs)) -> APP(app(sumwith, f), xs)

Furthermore, R contains one SCC.

R
DPs
→DP Problem 1
Remaining Obligation(s)

The following remains to be proven:
Dependency Pairs:

APP(app(sumwith, f), app(app(cons, x), xs)) -> APP(app(sumwith, f), xs)
APP(app(sumwith, f), app(app(cons, x), xs)) -> APP(f, x)
APP(app(sumwith, f), app(app(cons, x), xs)) -> APP(app(plus, app(f, x)), app(app(sumwith, f), xs))
APP(app(plus, app(s, x)), y) -> APP(app(plus, x), y)

Rules:

app(app(plus, 0), y) -> y
app(app(plus, app(s, x)), y) -> app(s, app(app(plus, x), y))
app(app(sumwith, f), nil) -> nil
app(app(sumwith, f), app(app(cons, x), xs)) -> app(app(plus, app(f, x)), app(app(sumwith, f), xs))

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