  Let $R = K[x_1, x_2, x_3, x_4]$ be the polynomial ring over a field of
characteristic zero. For the ideal $(x_1^a, x_2^b, x_3^c, x_4^d) \subset R$,
where at least one of $a$, $b$, $c$ and $d$ is equal to two, we prove that its
generic initial ideal with respect to the reverse lexicographic order is the
almost revlex ideal corresponding to the same Hilbert function.
