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(map,f),nil)  → nil
4:    app(app(map,f),app(app(cons,x),xs))  → app(app(cons,app(f,x)),app(app(map,f),xs))
5:    inc  → app(map,app(plus,app(s,0)))
There are 10 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(app(map,f),app(app(cons,x),xs))  → APP(app(cons,app(f,x)),app(app(map,f),xs))
10:    APP(app(map,f),app(app(cons,x),xs))  → APP(cons,app(f,x))
11:    APP(app(map,f),app(app(cons,x),xs))  → APP(f,x)
12:    APP(app(map,f),app(app(cons,x),xs))  → APP(app(map,f),xs)
13:    INC  → APP(map,app(plus,app(s,0)))
14:    INC  → APP(plus,app(s,0))
15:    INC  → APP(s,0)
The approximated dependency graph contains one SCC: {7,9,11,12}.
Tyrolean Termination Tool  (0.05 seconds)   ---  May 3, 2006