Öz
As a continues study of the paper [4], in here, we first state and prove
the p-Cockcroft property (or, equivalently, efficiency) for a presentation,
say PE, of the semi-direct product of a free abelian monoid rank two by
a finite cyclic monoid. Then, in a separate section, we present sufficient
conditions on a special case for PE to be minimal whilst it is inefficient.