Maintaining large and aging applications in a software house, with heterogeneous technologies, is very challenging. Whereas it is mandatory to continuously enhance user experience and maintain a good quality of service, the real business usage can be difficult to know precisely. To reach this goal, our project is to discover business models from the analysis of "logs". In this paper, we report on existing studies about applying process mining techniques and on our own experience with large datasets generated from daily end-user activities within an existing public services software. Our experiments led us to identify an interesting combination of features making our data hard to process with existing techniques. We conclude by providing perspectives to enable process discovery with such specific data.