Termination Proof Script

Consider the TRS R consisting of the rewrite rules
1:    app(app(map,f),nil)  → nil
2:    app(app(map,f),app(app(cons,x),xs))  → app(app(cons,app(f,x)),app(app(map,f),xs))
3:    app(app(treemap,f),app(app(node,x),xs))  → app(app(node,app(f,x)),app(app(map,app(treemap,f)),xs))
There are 9 dependency pairs:
4:    APP(app(map,f),app(app(cons,x),xs))  → APP(app(cons,app(f,x)),app(app(map,f),xs))
5:    APP(app(map,f),app(app(cons,x),xs))  → APP(cons,app(f,x))
6:    APP(app(map,f),app(app(cons,x),xs))  → APP(f,x)
7:    APP(app(map,f),app(app(cons,x),xs))  → APP(app(map,f),xs)
8:    APP(app(treemap,f),app(app(node,x),xs))  → APP(app(node,app(f,x)),app(app(map,app(treemap,f)),xs))
9:    APP(app(treemap,f),app(app(node,x),xs))  → APP(node,app(f,x))
10:    APP(app(treemap,f),app(app(node,x),xs))  → APP(f,x)
11:    APP(app(treemap,f),app(app(node,x),xs))  → APP(app(map,app(treemap,f)),xs)
12:    APP(app(treemap,f),app(app(node,x),xs))  → APP(map,app(treemap,f))
The approximated dependency graph contains one SCC: {4,6-8,10,11}.
Tyrolean Termination Tool  (0.12 seconds)   ---  May 3, 2006