  A semigroup variety is said to be a Rees-Sushkevich variety if it is
contained in a periodic variety generated by 0-simple semigroups. S. I.
Kublanovsky has proven that a variety V is a Rees-Sushkevich variety if and
only it does not contain any of special finite semigroups. These semigroups are
called indicator Burnside semigroups. It is shown that indicator Burnside
semigroups have polynomially decidable equational theory. Also it is shown that
each indicator Burnside semigroups generate a finitely based variety.
