Termination Proof Script

Consider the TRS R consisting of the rewrite rules
1:    app(app(app(fold,f),nil),x)  → x
2:    app(app(app(fold,f),app(app(cons,h),t)),x)  → app(app(app(fold,f),t),app(app(f,x),h))
3:    app(sum,l)  → app(app(app(fold,add),l),0)
4:    app(app(app(fold,mul),l),1)  → app(prod,l)
There are 8 dependency pairs:
5:    APP(app(app(fold,f),app(app(cons,h),t)),x)  → APP(app(app(fold,f),t),app(app(f,x),h))
6:    APP(app(app(fold,f),app(app(cons,h),t)),x)  → APP(app(fold,f),t)
7:    APP(app(app(fold,f),app(app(cons,h),t)),x)  → APP(app(f,x),h)
8:    APP(app(app(fold,f),app(app(cons,h),t)),x)  → APP(f,x)
9:    APP(sum,l)  → APP(app(app(fold,add),l),0)
10:    APP(sum,l)  → APP(app(fold,add),l)
11:    APP(sum,l)  → APP(fold,add)
12:    APP(app(app(fold,mul),l),1)  → APP(prod,l)
The approximated dependency graph contains one SCC: {5-10}.
Tyrolean Termination Tool  (0.02 seconds)   ---  May 3, 2006