Termination Proof Script

Consider the TRS R consisting of the rewrite rules
1:    app(app(mapt,f),app(leaf,x))  → app(leaf,app(f,x))
2:    app(app(mapt,f),app(node,xs))  → app(node,app(app(maptlist,f),xs))
3:    app(app(maptlist,f),nil)  → nil
4:    app(app(maptlist,f),app(app(cons,x),xs))  → app(app(cons,app(app(mapt,f),x)),app(app(maptlist,f),xs))
There are 10 dependency pairs:
5:    APP(app(mapt,f),app(leaf,x))  → APP(leaf,app(f,x))
6:    APP(app(mapt,f),app(leaf,x))  → APP(f,x)
7:    APP(app(mapt,f),app(node,xs))  → APP(node,app(app(maptlist,f),xs))
8:    APP(app(mapt,f),app(node,xs))  → APP(app(maptlist,f),xs)
9:    APP(app(mapt,f),app(node,xs))  → APP(maptlist,f)
10:    APP(app(maptlist,f),app(app(cons,x),xs))  → APP(app(cons,app(app(mapt,f),x)),app(app(maptlist,f),xs))
11:    APP(app(maptlist,f),app(app(cons,x),xs))  → APP(cons,app(app(mapt,f),x))
12:    APP(app(maptlist,f),app(app(cons,x),xs))  → APP(app(mapt,f),x)
13:    APP(app(maptlist,f),app(app(cons,x),xs))  → APP(mapt,f)
14:    APP(app(maptlist,f),app(app(cons,x),xs))  → APP(app(maptlist,f),xs)
The approximated dependency graph contains one SCC: {6,8,10,12,14}.
Tyrolean Termination Tool  (0.17 seconds)   ---  May 3, 2006