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