Consider the TRS R consisting of the rewrite rule

1: and(not(not(x)),y,not(z)) -> and(y,band(x,z),x)

There is one dependency pair:

2: AND(not(not(x)),y,not(z)) -> AND(y,band(x,z),x)

The approximated dependency graph contains one SCC:
{2}.

- Consider the SCC {2}.
There are no usable rules.
By taking the polynomial interpretation
[not](x) = x + 1,
[AND](x,y,z) = x + y + z + 1
and [band](x,y) = y + 1,
rule 2
is strictly decreasing.

Hence the TRS is terminating.