Termination Proof Script

Consider the TRS R consisting of the rewrite rules
1:    f(g(x),h(x),y,x)  → f(y,y,y,x)
2:    f(x,y,z,0)  → 2
3:    g(0)  → 2
4:    h(0)  → 2
There is one dependency pair:
5:    F(g(x),h(x),y,x)  → F(y,y,y,x)
The approximated dependency graph contains no SCCs and hence the TRS is trivially terminating.
Tyrolean Termination Tool  (0.00 seconds)   ---  May 3, 2006