Termination Proof Script

Consider the TRS R consisting of the rewrite rules
1:    app(app(map,f),nil)  → nil
2:    app(app(map,f),app(app(cons,x),xs))  → app(app(cons,app(f,x)),app(app(map,f),xs))
3:    app(app(minus,x),0)  → x
4:    app(app(minus,app(s,x)),app(s,y))  → app(app(minus,x),y)
5:    app(app(div,0),app(s,y))  → 0
6:    app(app(div,app(s,x)),app(s,y))  → app(s,app(app(div,app(app(minus,x),y)),app(s,y)))
There are 11 dependency pairs:
7:    APP(app(map,f),app(app(cons,x),xs))  → APP(app(cons,app(f,x)),app(app(map,f),xs))
8:    APP(app(map,f),app(app(cons,x),xs))  → APP(cons,app(f,x))
9:    APP(app(map,f),app(app(cons,x),xs))  → APP(f,x)
10:    APP(app(map,f),app(app(cons,x),xs))  → APP(app(map,f),xs)
11:    APP(app(minus,app(s,x)),app(s,y))  → APP(app(minus,x),y)
12:    APP(app(minus,app(s,x)),app(s,y))  → APP(minus,x)
13:    APP(app(div,app(s,x)),app(s,y))  → APP(s,app(app(div,app(app(minus,x),y)),app(s,y)))
14:    APP(app(div,app(s,x)),app(s,y))  → APP(app(div,app(app(minus,x),y)),app(s,y))
15:    APP(app(div,app(s,x)),app(s,y))  → APP(div,app(app(minus,x),y))
16:    APP(app(div,app(s,x)),app(s,y))  → APP(app(minus,x),y)
17:    APP(app(div,app(s,x)),app(s,y))  → APP(minus,x)
The approximated dependency graph contains one SCC: {7,9-11,14,16}.
Tyrolean Termination Tool  (0.13 seconds)   ---  May 3, 2006