Algorithm to test dependency preservation

Question

Is there an algorithm to test whether the decomposition of relation $R$ into relations $R_1,\dots,R_n$ is dependency-preserving?

In more detail, I am given a relation $R(x_1,\dots,x_m)$ on $m$ variables. I am given a decomposition of $R$ into relations $R_1,\dots,R_n$, where each relation $R_i$ refers to a subset of the variables $\{x_1,\dots,x_m\}$. I am also given a set of functional dependencies $F$ for $R$. I would like to know whether this decomposition is dependency-preserving. Is there an efficient algorithm to answer this question?

Recall the definition of "dependency-preserving" from database theory: the decomposition of $R$ into $R_1,\dots,R_n$ is dependency-preserving if $F^+=G^+$, where $G=G_1 \cup \dots \cup G_n$ and $G_i$ is the restriction of $F$ to the variables of $R_i$ (so $G_i$ is a set of functional dependencies for $R_i$).