Termination Proof Script

Consider the TRS R consisting of the rewrite rules
1:    app(app(plus,0),y)  → y
2:    app(app(plus,app(s,x)),y)  → app(s,app(app(plus,x),y))
3:    app(app(app(curry,f),x),y)  → app(app(f,x),y)
4:    add  → app(curry,plus)
There are 6 dependency pairs:
5:    APP(app(plus,app(s,x)),y)  → APP(s,app(app(plus,x),y))
6:    APP(app(plus,app(s,x)),y)  → APP(app(plus,x),y)
7:    APP(app(plus,app(s,x)),y)  → APP(plus,x)
8:    APP(app(app(curry,f),x),y)  → APP(app(f,x),y)
9:    APP(app(app(curry,f),x),y)  → APP(f,x)
10:    ADD  → APP(curry,plus)
The approximated dependency graph contains one SCC: {6,8,9}. Hence the TRS is terminating.
Tyrolean Termination Tool  (0.02 seconds)   ---  May 4, 2006