  One of the central problems in the study of parametrized constraint
satisfaction problems is the Dichotomy Conjecture by T. Feder and M. Vardi
stating that the constraint satisfaction problem (CSP) over a fixed, finite
constraint language is either solvable in polynomial time or
\textsc{NP}-complete. The conjecture was verified in certain special cases
(domains with a relatively small number of elements, constraint languages
containing all unary relations, etc.) In this article, we present a proof of
the Dichotomy Conjecture via local consistency and AF- consistency checks. In
fact, we show that, for every Taylor domain, which is
$(2\lceil\frac{K}{2}\rceil,3\lceil\frac{K}{2}\rceil)$-consistent, where $K$ is
the largest arity of a relation in the constraint language, we can define
polynomially many proper subinstances such that, the original instance of the
CSP is solvable if, and only if, the problem has a solution in one of those
subinstances.. Finally, a solution is constructed using the combination of SLAC
(Singleton Linear Arc Consistency), introduced by M. Kozik, and AF-consistency.
