Termination Proof Script

Consider the TRS R consisting of the rewrite rules
1:    app(app(plus,0),y)  → y
2:    app(app(plus,app(s,x)),y)  → app(s,app(app(plus,x),y))
3:    app(app(sumwith,f),nil)  → nil
4:    app(app(sumwith,f),app(app(cons,x),xs))  → app(app(plus,app(f,x)),app(app(sumwith,f),xs))
There are 7 dependency pairs:
5:    APP(app(plus,app(s,x)),y)  → APP(s,app(app(plus,x),y))
6:    APP(app(plus,app(s,x)),y)  → APP(app(plus,x),y)
7:    APP(app(plus,app(s,x)),y)  → APP(plus,x)
8:    APP(app(sumwith,f),app(app(cons,x),xs))  → APP(app(plus,app(f,x)),app(app(sumwith,f),xs))
9:    APP(app(sumwith,f),app(app(cons,x),xs))  → APP(plus,app(f,x))
10:    APP(app(sumwith,f),app(app(cons,x),xs))  → APP(f,x)
11:    APP(app(sumwith,f),app(app(cons,x),xs))  → APP(app(sumwith,f),xs)
The approximated dependency graph contains one SCC: {6,8,10,11}.
Tyrolean Termination Tool  (0.07 seconds)   ---  May 3, 2006