[Flenser]

  a = Appointment 1 start
  A = Appointment 1 end
  b = Appointment 2 start
  B = Appointment 2 end

The only predicates are: a < A, b < B

The complete set of orderings are thus:

  aAbB - no overlap
  bBaA - no overlap
  abAB - partial overlap
  baBA - partial overlap
  abBA - complete overlap of one appointment inside the other
  baAB - complete overlap of one appointment inside the other