Process mining is helpful for deploying new business processes as well as auditing, analyzing and improving the already enacted ones. Most of the existing process mining algorithms have some problems in dealing with invisible tasks, i.e., such tasks that exist in a process model but not in its event log. In this paper, a new process mining algorithm named a# is proposed, which extends the mining capability of the classical a algorithm by supporting the detection of prime invisible tasks from event logs. Prime invisible tasks are divided into five types according to their structural features, i.e., INITIALIZE, SKIP, REDO, SWITCH and FINALIZE. After that, a new ordering relation for detecting mendacious dependencies between tasks that reflect...