  For a first-order theory $T$, the Constraint Satisfaction Problem of $T$ is
the computational problem of deciding whether a given conjunction of atomic
formulas is satisfiable in some model of $T$. In this article we develop
sufficient conditions for polynomial-time tractability of the constraint
satisfaction problem for the union of two theories with disjoint relational
signatures. To this end, we introduce the concept of sampling for theories and
show that samplings can be applied to examples which are not covered by the
seminal result of Nelson and Oppen.
