Conformance checking (CC) techniques in process mining determine the conformity of cases, by means of their event sequences, with respect to a business process model. Online conformance checking (OCC) techniques perform such analysis for cases in event streams. Cases in streams may essentially not be concluded. Therefore, OCC techniques usually neglect the memory limitation and store all the observed cases whether seemingly concluded or unconcluded. Such indefinite storage of cases is inconsistent with the spirit of privacy regulations, such as GDPR, which advocate the retention of minimal data for a definite period of time. Catering to the aforementioned constraints, we propose two classes of novel approaches that partially or fully forget...