the $t$ view on the event timestamp.

### Lifecycle extension & Time extension

The XES standard [@Gunther2014] defines several lifecycle stages of a process. When an event log possesses both the lifecycle extension and the time extension, time differences can be calculated between different stages of the life cycle of a single activity. For a *complete* event for example, one could calculate the time difference with the associated *start* event of the same activity. Finding the associated *start* event becomes nontrivial when multiple instances of the same activity are in parallel, as it is then unknown which *complete* event belongs to which *start* event. We assume consecutive lifecycle steps of activities running in parallel to occur in the same order as the preceding lifecycle step. For example, when we observe two *start* events of an activity of type *A* in a row, followed by two *complete* events of type *A*, we assume the first *complete* to belong to the first *start*, and the second *complete* to belong to the second *start*.

We estimate a Gaussian Mixture Model (GMM) for each tuple of two lifecycle steps for a certain activity on the time differences between those two lifecycle steps for this 