Term Rewriting System R:
[f, g, x]
app(app(app(comp, f), g), x) -> app(f, app(g, x))
app(twice, f) -> app(app(comp, f), f)

Termination of R to be shown. 



   R
     ↳Dependency Pair Analysis



R contains the following Dependency Pairs:

APP(app(app(comp, f), g), x) -> APP(f, app(g, x))
APP(app(app(comp, f), g), x) -> APP(g, x)
APP(twice, f) -> APP(app(comp, f), f)
APP(twice, f) -> APP(comp, f)

Furthermore, R contains one SCC. 


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




The following remains to be proven:
Dependency Pairs:

APP(twice, f) -> APP(app(comp, f), f)
APP(app(app(comp, f), g), x) -> APP(g, x)
APP(app(app(comp, f), g), x) -> APP(f, app(g, x))


Rules:


app(app(app(comp, f), g), x) -> app(f, app(g, x))
app(twice, f) -> app(app(comp, f), f)




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