Termination Proof Script

Consider the TRS R consisting of the rewrite rules
1:    app(app(app(if,true),x),y)  → x
2:    app(app(app(if,false),x),y)  → y
3:    app(app(filter,f),nil)  → nil
4:    app(app(filter,f),app(app(cons,x),xs))  → app(app(app(if,app(f,x)),app(app(cons,x),app(app(filter,f),xs))),app(app(filter,f),xs))
There are 6 dependency pairs:
5:    APP(app(filter,f),app(app(cons,x),xs))  → APP(app(app(if,app(f,x)),app(app(cons,x),app(app(filter,f),xs))),app(app(filter,f),xs))
6:    APP(app(filter,f),app(app(cons,x),xs))  → APP(app(if,app(f,x)),app(app(cons,x),app(app(filter,f),xs)))
7:    APP(app(filter,f),app(app(cons,x),xs))  → APP(if,app(f,x))
8:    APP(app(filter,f),app(app(cons,x),xs))  → APP(f,x)
9:    APP(app(filter,f),app(app(cons,x),xs))  → APP(app(cons,x),app(app(filter,f),xs))
10:    APP(app(filter,f),app(app(cons,x),xs))  → APP(app(filter,f),xs)
The approximated dependency graph contains one SCC: {5,6,8,10}.
Tyrolean Termination Tool  (0.09 seconds)   ---  May 3, 2006