Termination Proof Script

Consider the TRS R consisting of the rewrite rules
1:    app(app(app(consif,true),x),ys)  → app(app(cons,x),ys)
2:    app(app(app(consif,false),x),ys)  → ys
3:    app(app(filter,f),nil)  → nil
4:    app(app(filter,f),app(app(cons,x),xs))  → app(app(app(consif,app(f,x)),x),app(app(filter,f),xs))
There are 7 dependency pairs:
5:    APP(app(app(consif,true),x),ys)  → APP(app(cons,x),ys)
6:    APP(app(app(consif,true),x),ys)  → APP(cons,x)
7:    APP(app(filter,f),app(app(cons,x),xs))  → APP(app(app(consif,app(f,x)),x),app(app(filter,f),xs))
8:    APP(app(filter,f),app(app(cons,x),xs))  → APP(app(consif,app(f,x)),x)
9:    APP(app(filter,f),app(app(cons,x),xs))  → APP(consif,app(f,x))
10:    APP(app(filter,f),app(app(cons,x),xs))  → APP(f,x)
11:    APP(app(filter,f),app(app(cons,x),xs))  → APP(app(filter,f),xs)
The approximated dependency graph contains one SCC: {5,7,8,10,11}.
Tyrolean Termination Tool  (0.10 seconds)   ---  May 3, 2006