Termination Proof Script

Consider the TRS R consisting of the rewrite rules
1:    app(app(neq,0),0)  → false
2:    app(app(neq,0),app(s,y))  → true
3:    app(app(neq,app(s,x)),0)  → true
4:    app(app(neq,app(s,x)),app(s,y))  → app(app(neq,x),y)
5:    app(app(filter,f),nil)  → nil
6:    app(app(filter,f),app(app(cons,y),ys))  → app(app(app(filtersub,app(f,y)),f),app(app(cons,y),ys))
7:    app(app(app(filtersub,true),f),app(app(cons,y),ys))  → app(app(cons,y),app(app(filter,f),ys))
8:    app(app(app(filtersub,false),f),app(app(cons,y),ys))  → app(app(filter,f),ys)
9:    nonzero  → app(filter,app(neq,0))
There are 13 dependency pairs:
10:    APP(app(neq,app(s,x)),app(s,y))  → APP(app(neq,x),y)
11:    APP(app(neq,app(s,x)),app(s,y))  → APP(neq,x)
12:    APP(app(filter,f),app(app(cons,y),ys))  → APP(app(app(filtersub,app(f,y)),f),app(app(cons,y),ys))
13:    APP(app(filter,f),app(app(cons,y),ys))  → APP(app(filtersub,app(f,y)),f)
14:    APP(app(filter,f),app(app(cons,y),ys))  → APP(filtersub,app(f,y))
15:    APP(app(filter,f),app(app(cons,y),ys))  → APP(f,y)
16:    APP(app(app(filtersub,true),f),app(app(cons,y),ys))  → APP(app(cons,y),app(app(filter,f),ys))
17:    APP(app(app(filtersub,true),f),app(app(cons,y),ys))  → APP(app(filter,f),ys)
18:    APP(app(app(filtersub,true),f),app(app(cons,y),ys))  → APP(filter,f)
19:    APP(app(app(filtersub,false),f),app(app(cons,y),ys))  → APP(app(filter,f),ys)
20:    APP(app(app(filtersub,false),f),app(app(cons,y),ys))  → APP(filter,f)
21:    NONZERO  → APP(filter,app(neq,0))
22:    NONZERO  → APP(neq,0)
The approximated dependency graph contains one SCC: {10,12,13,15,17,19}.
Tyrolean Termination Tool  (0.22 seconds)   ---  May 3, 2006