Termination Proof Script

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