  We investigate Mal'cev conditions described by equations whose variables runs
over the set of all compatible reflexive relations. Let $p \leq q$ be an
equation in the language $\{\wedge, \circ,+\}$. We give a characterization of
the class of all varieties which satisfy $p \leq q$ 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 compatible reflexive relations, and to characterize when an equation $p
\leq q$ expresses the same property when considered over the congruence
lattices or over the sets of all compatible reflexive relations of algebras in
a variety.
