In theorem prover or SMT solver based verification, the program to be verified is often given in an intermediate verification language such as Boogie, Why, or CHC. This setting raises new challenges. We investigate a preprocessing step which takes the similar role that alias analysis plays in verification, except that now, a (mathematical) map is used to model the memory or a data object of type array. We present a program transformation that takes a program P to an equivalent program P' such that, by verifying P' instead of P, we can reduce the burden of the exponential explosion in the number of case splits. Here, the case splits are according to whether two statements using the same map variable are independent or not; if they are independent, we might as well employ two different map variables and thus remove the need for a case split (this is the idea behind the program transformation). We have implemented the program transformation and show that, in an ideal case, we can avoid the exponential explosion.