monomial orders

I'm reading a book on polynomials and the section on 'monomial order'. They
give an example of a multivariate polynomial ordered in 3 different ways -
they being lexicographic, graded lexicographic, and graded reverse
lexicographic order.

The polynomial is f = 4xyz^2 + 4x^3 - 5y^4 + 7xy^2z

It states that in lexicographic order this is :-

4x^3 + 7xy^2z + 4xyz^2 - 5y^4

and graded lexicographic is :-

7xy^2z + 4xyz^2 - 5y^4 + 4x^3

and in graded reverse lexicographic it makes it as :-

-5y^4 + 7xy^2z + 4xyz^2 + 4x^3

but surely this should be :-
-5y^4 + 4xyz^2 + 7xy^2z + 4x^3 ??


Any help appreciated


.