Conformance checking confronts process models with real process executions to detect and measure deviations between modelled and observed behaviour. The core technique for conformance checking is the computation of an alignment. Current approaches for alignment computation rely on a shortest-path technique over the product of the state-space of a model and the observed trace, thus suffering from the well-known state explosion problem. This paper presents a fresh alternative for alignment computation of acyclic process models, that encodes the alignment problem as a Constraint Satisfaction Problem. Since modern solvers for this framework are capable of dealing with large instances, this contribution has a clear potential. Remarkably, our pro...