A difference semigroup is an algebra \((S;\cdot,-)\) with two binary operations, \(\cdot\) and \(-\), such that \((S;\cdot)\) is a semigroup, \((S;-)\) satisfies the identities \(x-(y-x)=x\), \(x-(x-y)=y-(y-x)\), \((x-y)-z=(x-z)-y\), and multiplication \(\cdot\) distributes (on both sides) over subtraction. The reviewer [Commun. Algebra 20, No. 8, 2153-2169 (1992; Zbl 0798.20058)] proposed the problem of characterizing semigroup reducts \((S;\cdot)\) of subtraction semigroups. The author solves a very particular case of this problem (for semigroups with zero 0 and subtraction such that \(x-x=0\) and \(x-y=x\) for \(x\neq y\)).