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,app(p,app(s,x))),app(p,app(s,y)))
5:    app(p,app(s,x))  → x
6:    app(app(div,0),app(s,y))  → 0
7:    app(app(div,app(s,x)),app(s,y))  → app(s,app(app(div,app(app(minus,x),y)),app(s,y)))
There are 13 dependency pairs:
8:    APP(app(map,f),app(app(cons,x),xs))  → APP(app(cons,app(f,x)),app(app(map,f),xs))
9:    APP(app(map,f),app(app(cons,x),xs))  → APP(cons,app(f,x))
10:    APP(app(map,f),app(app(cons,x),xs))  → APP(f,x)
11:    APP(app(map,f),app(app(cons,x),xs))  → APP(app(map,f),xs)
12:    APP(app(minus,app(s,x)),app(s,y))  → APP(app(minus,app(p,app(s,x))),app(p,app(s,y)))
13:    APP(app(minus,app(s,x)),app(s,y))  → APP(minus,app(p,app(s,x)))
14:    APP(app(minus,app(s,x)),app(s,y))  → APP(p,app(s,x))
15:    APP(app(minus,app(s,x)),app(s,y))  → APP(p,app(s,y))
16:    APP(app(div,app(s,x)),app(s,y))  → APP(s,app(app(div,app(app(minus,x),y)),app(s,y)))
17:    APP(app(div,app(s,x)),app(s,y))  → APP(app(div,app(app(minus,x),y)),app(s,y))
18:    APP(app(div,app(s,x)),app(s,y))  → APP(div,app(app(minus,x),y))
19:    APP(app(div,app(s,x)),app(s,y))  → APP(app(minus,x),y)
20:    APP(app(div,app(s,x)),app(s,y))  → APP(minus,x)
The approximated dependency graph contains one SCC: {8,10-12,17,19}.
Tyrolean Termination Tool  (0.18 seconds)   ---  May 3, 2006