Term Rewriting System R:
[f, x]
app(app(F, app(app(F, f), x)), x) -> app(app(F, app(G, app(app(F, f), x))), app(f, x))

Innermost Termination of R to be shown. 



   R
     ↳Dependency Pair Analysis



R contains the following Dependency Pairs:

APP(app(F, app(app(F, f), x)), x) -> APP(app(F, app(G, app(app(F, f), x))), app(f, x))
APP(app(F, app(app(F, f), x)), x) -> APP(F, app(G, app(app(F, f), x)))
APP(app(F, app(app(F, f), x)), x) -> APP(G, app(app(F, f), x))
APP(app(F, app(app(F, f), x)), x) -> APP(f, x)

Furthermore, R contains one SCC. 


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




The following remains to be proven:
Dependency Pairs:

APP(app(F, app(app(F, f), x)), x) -> APP(f, x)
APP(app(F, app(app(F, f), x)), x) -> APP(app(F, app(G, app(app(F, f), x))), app(f, x))


Rule:


app(app(F, app(app(F, f), x)), x) -> app(app(F, app(G, app(app(F, f), x))), app(f, x))


Strategy:

innermost



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