AbstractWe investigate Mal'cev conditions described by those equations whose variables runs over the set of all compatible reflexive relations. Let $$p \le q$$ p ≤ q be an equation for the language $$\{\wedge , \circ ,+\}$$ { ∧ , ∘ , + } . We give a characterization of the class of all varieties which satisfy $$p \le q$$ p ≤ q over the set of all compatible reflexive relations. The aim is to find an analogon of the Pixley–Wille algorithm for conditions expressed by equations over the set of all

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... compatible reflexive relations, and to characterize when an equation $$p \le q$$ p ≤ q expresses the same property when considered over the congruence lattices or over the sets of all compatible reflexive relations of algebras in a variety.