I agree with Lucas K's approach. For this situation, it seems the most logical working with the machine data that is available which are logs of system activity for all employees. I'm assuming each employee has a specific login/ID # associated with them to track every activity across all systems. Each activity log should have a timestamp which can be used to measure and determine if they met the Block Leave requirement.
For the last question in your post @carolynmcdonoughtest, is that really relevant since it's required that they "did not use any systems during that entire 14-day period"?
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