Consider the TRS R consisting of the rewrite rules

1: implies(not(x),y) -> or(x,y)
2: implies(not(x),or(y,z)) -> implies(y,or(x,z))
3: implies(x,or(y,z)) -> or(y,implies(x,z))

There are 2 dependency pairs:

4: IMPLIES(not(x),or(y,z)) -> IMPLIES(y,or(x,z))
5: IMPLIES(x,or(y,z)) -> IMPLIES(x,z)

The approximated dependency graph contains one SCC:
{4,5}.

- Consider the SCC {4,5}.
There are no usable rules.
By taking the polynomial interpretation
[not](x) = x + 1
and [IMPLIES](x,y) = [or](x,y) = x + y + 1,
the rules in {4,5}
are strictly decreasing.

Hence the TRS is terminating.