  In this paper, we investigate the reducibility property of semidirect
products of the form $\bf V*\bf D$ relatively to (pointlike) systems of
equations of the form $x_1=\cdots=x_n$, where $\bf D$ denotes the pseudovariety
of definite semigroups. We establish a connection between pointlike
reducibility of $\bf V*\bf D$ and the pointlike reducibility of the
pseudovariety $\bf V$. In particular, for the canonical signature $\kappa$
consisting of the multiplication and the $(\omega-1)$-power, we show that $\bf
V*\bf D$ is pointlike $\kappa$-reducible when $\bf V$ is pointlike
$\kappa$-reducible.
