Termination Proof Script

Consider the TRS R consisting of the rewrite rules
1:    app(app(,x),x)  → e
2:    app(app(,e),x)  → x
3:    app(app(,x),app(app(.,x),y))  → y
4:    app(app(,app(app(/,x),y)),x)  → y
5:    app(app(/,x),x)  → e
6:    app(app(/,x),e)  → x
7:    app(app(/,app(app(.,y),x)),x)  → y
8:    app(app(/,x),app(app(,y),x))  → y
9:    app(app(.,e),x)  → x
10:    app(app(.,x),e)  → x
11:    app(app(.,x),app(app(,x),y))  → y
12:    app(app(.,app(app(/,y),x)),x)  → y
There are no dependency pairs. Hence the TRS is trivially terminating.
Tyrolean Termination Tool  (0.02 seconds)   ---  May 3, 2006