Embodiments of the present disclosure involve determining, for each package required for execution of an application, the lowest version that is compatible with a dependency specification of the package. For each of a set of packages required to execute an application: analyzing a dependency specification corresponding to the package to determine a set of relations, the set of relations defining version numbers of the package that are compatible with the application. The set of relations may be desugared to generate a basic format set of relations, and conflicting relations may be removed from the basic format set of relations. Duplicate relations may also be removed from the basic format set of relations to generate a deduplicated set of relations. A lowest version of the package that is compatible with the dependency specification may be determined based on operators used among the deduplicated set of relations.