Consider the TRS R consisting of the rewrite rule
1: f(g(X)) -> f(X)
There is one dependency pair:
2: F(g(X)) -> F(X)
The approximated dependency graph contains one SCC:
{2}.
- Consider the SCC {2}.
There are no usable rules.
By taking the polynomial interpretation
[F](x) = [g](x) = x + 1,
rule 2
is strictly decreasing.
Hence the TRS is terminating.