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Process mining techniques relate observed behavior to modeled behavior, eg, the automatic discovery of a Petri net based on an event log. Process mining is not limited to process discovery and also includes conformance checking. Conformance checking techniques are used for evaluating the quality of discovered process models and to diagnose deviations from some normative model (eg, to check compliance). Existing conformance checking approaches typically focus on the control flow, thus being unable to diagnose deviations concerning data. This paper proposes a technique to check the conformance of data-aware process models. We use so-called" data Petri nets" to model data variables, guards, and read/write actions. Additional perspectives such as resource allocation and time constraints can be encoded in terms of variables. Data-aware conformance checking problem may be very time consuming and sometimes even intractable when there are many transitions and data variables. Therefore, we propose a technique to decompose large data-aware conformance checking problems into smaller problems that can be solved more efficiently. We provide a general correctness result showing that decomposition does not influence the outcome of conformance checking. Moreover, two decomposition strategies are presented. The approach is supported through ProM plug-ins and experimental results show that significant performance improvements are indeed possible.