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(inc,xs)  → app(app(map,app(plus,app(s,0))),xs)
4:    app(app(map,f),nil)  → nil
5:    app(app(map,f),app(app(cons,x),xs))  → app(app(cons,app(f,x)),app(app(map,f),xs))
There are 11 dependency pairs:
6:    APP(app(plus,app(s,x)),y)  → APP(s,app(app(plus,x),y))
7:    APP(app(plus,app(s,x)),y)  → APP(app(plus,x),y)
8:    APP(app(plus,app(s,x)),y)  → APP(plus,x)
9:    APP(inc,xs)  → APP(app(map,app(plus,app(s,0))),xs)
10:    APP(inc,xs)  → APP(map,app(plus,app(s,0)))
11:    APP(inc,xs)  → APP(plus,app(s,0))
12:    APP(inc,xs)  → APP(s,0)
13:    APP(app(map,f),app(app(cons,x),xs))  → APP(app(cons,app(f,x)),app(app(map,f),xs))
14:    APP(app(map,f),app(app(cons,x),xs))  → APP(cons,app(f,x))
15:    APP(app(map,f),app(app(cons,x),xs))  → APP(f,x)
16:    APP(app(map,f),app(app(cons,x),xs))  → APP(app(map,f),xs)
The approximated dependency graph contains one SCC: {7,9,13,15,16}.
Tyrolean Termination Tool  (0.14 seconds)   ---  May 3, 2006