In this paper, we investigate the reducibility property of semidirect products of the form [Formula: see text] relatively to (pointlike) systems of equations of the form [Formula: see text], where [Formula: see text] d̃enotes the pseudovariety of definite semigroups. We establish a connection between pointlike reducibility of [Formula: see text] and the pointlike reducibility of the pseudovariety [Formula: see text]. In particular, for the canonical signature [Formula: see text] consisting of the multiplication and the [Formula: see text]-power, we show that [Formula: see text] is pointlike [Formula: see text]-reducible when [Formula: see text] is pointlike [Formula: see text]-reducible.