Termination Proof Script

Consider the TRS R consisting of the rewrite rules
1:    app(app(times,x),0)  → 0
2:    app(app(times,x),app(s,y))  → app(app(plus,app(app(times,x),y)),x)
3:    app(app(plus,x),0)  → x
4:    app(app(plus,0),x)  → x
5:    app(app(plus,x),app(s,y))  → app(s,app(app(plus,x),y))
6:    app(app(plus,app(s,x)),y)  → app(s,app(app(plus,x),y))
There are 8 dependency pairs:
7:    APP(app(times,x),app(s,y))  → APP(app(plus,app(app(times,x),y)),x)
8:    APP(app(times,x),app(s,y))  → APP(plus,app(app(times,x),y))
9:    APP(app(times,x),app(s,y))  → APP(app(times,x),y)
10:    APP(app(plus,x),app(s,y))  → APP(s,app(app(plus,x),y))
11:    APP(app(plus,x),app(s,y))  → APP(app(plus,x),y)
12:    APP(app(plus,app(s,x)),y)  → APP(s,app(app(plus,x),y))
13:    APP(app(plus,app(s,x)),y)  → APP(app(plus,x),y)
14:    APP(app(plus,app(s,x)),y)  → APP(plus,x)
The approximated dependency graph contains one SCC: {7,9,11,13}.
Tyrolean Termination Tool  (0.03 seconds)   ---  May 3, 2006