Conformance checking is the problem of verifying if the actual executions of business processes, which are recorded by information systems in dedicated event logs, are compliant with a process model that encodes the process' constraints. Within conformance checking, alignment-based techniques can exactly pinpoint where deviations are observed. Existing alignment-based techniques rely on the assumption of a perfect knowledge of the order with which process' activities were executed in reality. However, experience shows that, due to logging errors and inaccuracies, it is not always possible to determine the exact order with which certain activities were executed. This paper illustrates an alignment-based technique where the perfect knowledge assumption of the execution's order is removed. The technique transforms the problem of alignment-based conformance checking into a planning problem encoded in PDDL, for which planners can find a correct solution in a finite amount of time. We implemented the technique as a software tool that is integrated with state-of-the-art planners. To showcase its practical relevance and scalability, we report on experiments with a real-life case study and several synthetic ones of increasing complexity.