A running process instance may have a termination date in the future.
While configuring the Dimensions view
to monitor the historical data of a process, you have selected the Termination
Time dimension, to be a row, column or page dimension. While viewing the your
multidimensional analysis for that process, you may find that a running process
instance has a termination date of 01/01/9999. This does not mean that your
process is terminated. This is a placeholder date till the process instance
actually terminates and its data is replicated from the Runtime
database to the Historical database (by default every 24 hours). When the
process terminates, the 01/01/9999 date will be replaced with the actual date
of its termination.