The execution of (business) processes generates valuable traces of event data in the information systems employed within companies. Recently, approaches for monitoring the correctness of the execution of running processes have been developed in the area of process mining, i.e., online conformance checking. The advantages of monitoring a process' conformity during its execution are clear, i.e., deviations are detected as soon as they occur and countermeasures can immediately be initiated to reduce the possible negative effects caused by process deviations. Existing work in online conformance checking only allows for obtaining approximations of non-conformity, e.g., overestimating the actual severity of the deviation. In this paper, we present an exact, parameter-free, online conformance checking algorithm that computes conformance checking results on the fly. Our algorithm exploits the fact that the conformance checking problem can be reduced to a shortest path problem, by incrementally expanding the search space and reusing previously computed intermediate results. Our experiments show that our algorithm outperforms comparable state-of-the-art approximation algorithms.