  There are two well known types of algorithms for solving CSPs: local
propagation and generating a basis of the solution space. For several years the
focus of the CSP research has been on `hybrid' algorithms that somehow combine
the two approaches. In this paper we present a new method of such hybridization
that allows us to solve certain CSPs that has been out of reach for a quite a
while. We consider these method on a fairly restricted class of CSPs given by
algebras we will call semilattice block Mal'tsev. An algebra A is called
semilattice block Mal'tsev if it has a binary operation f, a ternary operation
m, and a congruence s such that the quotient A/s with operation $f$ is a
semilattice, $f$ is a projection on every block of s, and every block of s is a
Mal'tsev algebra with Mal'tsev operation m. We show that the constraint
satisfaction problem over a semilattice block Mal'tsev algebra is solvable in
polynomial time.
