Termination Proof Script

Consider the TRS R consisting of the rewrite rules
1:    app(app(twice,f),x)  → app(f,app(f,x))
2:    app(app(map,f),nil)  → nil
3:    app(app(map,f),app(app(cons,h),t))  → app(app(cons,app(f,h)),app(app(map,f),t))
4:    app(app(fmap,nil),x)  → nil
5:    app(app(fmap,app(app(cons,f),t_f)),x)  → app(app(cons,app(f,x)),app(app(fmap,t_f),x))
There are 11 dependency pairs:
6:    APP(app(twice,f),x)  → APP(f,app(f,x))
7:    APP(app(twice,f),x)  → APP(f,x)
8:    APP(app(map,f),app(app(cons,h),t))  → APP(app(cons,app(f,h)),app(app(map,f),t))
9:    APP(app(map,f),app(app(cons,h),t))  → APP(cons,app(f,h))
10:    APP(app(map,f),app(app(cons,h),t))  → APP(f,h)
11:    APP(app(map,f),app(app(cons,h),t))  → APP(app(map,f),t)
12:    APP(app(fmap,app(app(cons,f),t_f)),x)  → APP(app(cons,app(f,x)),app(app(fmap,t_f),x))
13:    APP(app(fmap,app(app(cons,f),t_f)),x)  → APP(cons,app(f,x))
14:    APP(app(fmap,app(app(cons,f),t_f)),x)  → APP(f,x)
15:    APP(app(fmap,app(app(cons,f),t_f)),x)  → APP(app(fmap,t_f),x)
16:    APP(app(fmap,app(app(cons,f),t_f)),x)  → APP(fmap,t_f)
The approximated dependency graph contains one SCC: {6-8,10-12,14,15}.
Tyrolean Termination Tool  (0.13 seconds)   ---  May 3, 2006