completely reduced form of (see page 6) and not just a normal form. if we want to find a normal form of in that example it will be but we can also reduce
completely: you see is the one that the example gives. the S polynomials found in the second and third examples in page 7 are not correct.
for example in the second example we actually have: the authors forgot about 4 in the denominator.
you should also take a look at this, which is written by the creator of Grobner bases.