Termination Proof Script

Consider the TRS R consisting of the rewrite rules
1:    app(app(f,0),n)  → app(app(hd,app(app(map,f),app(app(cons,0),nil))),n)
2:    app(app(map,f),nil)  → nil
3:    app(app(map,f),app(app(cons,x),xs))  → app(app(cons,app(f,x)),app(app(map,f),xs))
There are 10 dependency pairs:
4:    APP(app(f,0),n)  → APP(app(hd,app(app(map,f),app(app(cons,0),nil))),n)
5:    APP(app(f,0),n)  → APP(hd,app(app(map,f),app(app(cons,0),nil)))
6:    APP(app(f,0),n)  → APP(app(map,f),app(app(cons,0),nil))
7:    APP(app(f,0),n)  → APP(map,f)
8:    APP(app(f,0),n)  → APP(app(cons,0),nil)
9:    APP(app(f,0),n)  → APP(cons,0)
10:    APP(app(map,f),app(app(cons,x),xs))  → APP(app(cons,app(f,x)),app(app(map,f),xs))
11:    APP(app(map,f),app(app(cons,x),xs))  → APP(cons,app(f,x))
12:    APP(app(map,f),app(app(cons,x),xs))  → APP(f,x)
13:    APP(app(map,f),app(app(cons,x),xs))  → APP(app(map,f),xs)
The approximated dependency graph contains one SCC: {4,6,8,10,12,13}.
Tyrolean Termination Tool  (0.08 seconds)   ---  May 3, 2006