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

Innermost Termination of R to be shown. 



   R
     ↳Dependency Pair Analysis



R contains the following Dependency Pairs:

APP(f, app(g, x)) -> APP(g, app(f, app(f, x)))
APP(f, app(g, x)) -> APP(f, app(f, x))
APP(f, app(g, x)) -> APP(f, x)
APP(f, app(h, x)) -> APP(h, app(g, x))
APP(f, app(h, x)) -> APP(g, x)

Furthermore, R contains one SCC. 


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




The following remains to be proven:
Dependency Pairs:

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


Rules:


app(f, app(g, x)) -> app(g, app(f, app(f, x)))
app(f, app(h, x)) -> app(h, app(g, x))


Strategy:

innermost



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