Termination Proof Script

Consider the TRS R consisting of the rewrite rules
1:    f(a,x)  → g(a,x)
2:    g(a,x)  → f(b,x)
3:    f(a,x)  → f(b,x)
There are 3 dependency pairs:
4:    F(a,x)  → G(a,x)
5:    G(a,x)  → F(b,x)
6:    F(a,x)  → F(b,x)
The approximated dependency graph contains no SCCs and hence the TRS is trivially terminating.
Tyrolean Termination Tool  (0.01 seconds)   ---  May 3, 2006