Term Rewriting System R:
[x, y]
app(app(times, x), 0) -> 0
app(app(times, x), app(s, y)) -> app(app(plus, app(app(times, x), y)), x)
app(app(plus, x), 0) -> x
app(app(plus, 0), x) -> x
app(app(plus, x), app(s, y)) -> app(s, app(app(plus, x), y))
app(app(plus, app(s, x)), y) -> app(s, app(app(plus, x), y))

Termination of R to be shown. 



   R
     ↳Dependency Pair Analysis



R contains the following Dependency Pairs:

APP(app(times, x), app(s, y)) -> APP(app(plus, app(app(times, x), y)), x)
APP(app(times, x), app(s, y)) -> APP(plus, app(app(times, x), y))
APP(app(times, x), app(s, y)) -> APP(app(times, x), y)
APP(app(plus, x), app(s, y)) -> APP(s, app(app(plus, x), y))
APP(app(plus, x), app(s, y)) -> APP(app(plus, x), y)
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)

Furthermore, R contains one SCC. 


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




The following remains to be proven:
Dependency Pairs:

APP(app(plus, app(s, x)), y) -> APP(app(plus, x), y)
APP(app(plus, x), app(s, y)) -> APP(app(plus, x), y)
APP(app(times, x), app(s, y)) -> APP(app(times, x), y)
APP(app(times, x), app(s, y)) -> APP(app(plus, app(app(times, x), y)), x)


Rules:


app(app(times, x), 0) -> 0
app(app(times, x), app(s, y)) -> app(app(plus, app(app(times, x), y)), x)
app(app(plus, x), 0) -> x
app(app(plus, 0), x) -> x
app(app(plus, x), app(s, y)) -> app(s, app(app(plus, x), y))
app(app(plus, app(s, x)), y) -> app(s, app(app(plus, x), y))




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