Efficient consistency maintenance of incomplete and dynamic real-life databases is a quality label for further data analysis. In prior work, we tackled the generic problem of database updating in the presence of tuple generating constraints from a theoretical viewpoint. The current paper considers the usability of our approach by (a) introducing incremental update routines (instead of the previous from-scratch versions) and (b) removing the restriction that limits the contents of the database to fit in the main memory. In doing so, this paper offers new algorithms, proposes queries and data models inviting discussions on the representation of incompleteness on databases. We also propose implementations under a graph database model and the traditional relational database model. Our experiments show that computation times are similar globally but point to discrepancies in some steps.