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This paper is a contribution to the investigation of hyperstructures in connection with binary relations, i.e. to one of the areas covered by canonical books on hyperstructure theory. We use a construction of hyperstructures from quasi- or partially ordered semigroups and study cases which result in semihypergroups such that the reproductive law does not hold. First, such cases are identified. Then we study some of their properties. Examples as well as some applications on isolated particular results obtained earlier without the theoretical background of this paper are included.
