Denote by RUD the set of all rudimentary functions, together with the function that takes any **set** to its transitive closure.

Assume that I know that a binary relation $R$ is definable by some function in RUD. Is there a way to define $R^+$, the transitive closure of the **relation** $R$, using functions in RUD? Maybe there isn't one, but I strongly feel there should be a way and I cannot seem to find it.
I can be even more specific, I want to be able to define the function that given a set $x$ returns the set $\{ y | R^+(x,y) \}$, given that I know there is a function in RUD which defines the function that takes $x$ to $\{ y | R(x,y) \}$.

Thanks for your help!