A data-dependent process (DDP) models an application whose control flow is guided by a finite state machine, as well as by the state of an underlying database. DDPs are commonly found e.g., in e-commerce. In this paper we develop a framework supporting the use of provenance in static (temporal) analysis of possible DDP executions. Using provenance support, analysts can interactively test and explore the effect of hypothetical modifications to a DDP's state machine and/or to the underlying database. They can also extend the analysis to incorporate the propagation of annotations from meta-domains of interest, e.g., cost or access privileges.Toward this goal we note that the framework of semiringbased provenance was proven highly effective in fulfilling similar needs in the context of database queries. In this paper we consider novel constructions that generalize the semiring approach to the context of DDP analysis. These constructions address two interacting new challenges: (1) to combine provenance annotations for both information that resides in the database and information about external inputs (e.g., user choices), and (2) to finitely capture infinite process executions. We analyze our solution from theoretical and experimental perspectives, proving its effectiveness.