Consider the TRS R consisting of the rewrite rules
1:
p(f(f(x)))
→ q(f(g(x)))
2:
p(g(g(x)))
→ q(g(f(x)))
3:
q(f(f(x)))
→ p(f(g(x)))
4:
q(g(g(x)))
→ p(g(f(x)))
There are 4 dependency pairs:
5:
P(f(f(x)))
→ Q(f(g(x)))
6:
P(g(g(x)))
→ Q(g(f(x)))
7:
Q(f(f(x)))
→ P(f(g(x)))
8:
Q(g(g(x)))
→ P(g(f(x)))
The approximated dependency graph contains no SCCs
and hence the TRS is trivially terminating.
Tyrolean Termination Tool (0.00 seconds)
--- May 4, 2006