Regression verification is an approach complementing regression testing with formal verification. The goal is to formally prove that two versions of a program behave either equally or differently in a precisely specified way. In this paper, we present a novel automatic approach for regression verification that reduces the equivalence of two related imperative integer programs to Horn constraints over uninterpreted predicates. Subsequently, state-of-the-art SMT solvers are used to solve the constraints. We have implemented the approach, and our experiments show non-trivial integer programs that can now be proved equivalent without further user input.