We now show how the result size - and therefore also the selectivity
factor according to (11.1) - of the elementary
temporal joins of table 11.1 can be calculated. For
notational purposes, we assume that the selectivity factor / result
size of some join 
is to be derived. The set comprises the interval start- and endpoints of
all the rows in both of the relations that participate in the join,
i.e. R and Q.
In the case of a start join we are
looking for combinations 
of tuples 
and 
whose timestamps start at the same time. There are
tuples in R and tuples in Q that start at a
timepoint t. As for all we can concentrate on the tj for .Considering that any timestamp has exactly one startpoint, we know
that there are no redundant counts, therefore the result size can be
computed by summing up the numbers. Thus the result size of a start
join is
A before join requires a timestamp of a tuple r to end before the timestamp of q starts if they are to be combined and put into the join result. Thus those tuples in R that end at timepoint t combine with all those tuples in Q that start after t, i.e.
tuple combinations arise from that. Alternatively, one could consider those tuples in Q that start at t. They join with all tuples in R that have ended before t, i.e. tuple combinations arise from that. As above and for the same reasons we can concentrate on those t that are start- and endpoints. Thus the result size of a before join is As the after join is an inverted before join, its result size is derived similarly as Finally, a left-overlap join requires an r's timestamp's startpoint to lie inside the timestamp of a q if they are to qualify for the result. At a timepoint t these are tuples. Similarly, a right-overlap join requires an r's timestamp's endpoint to lie inside the timestamp of a q if they are to qualify for the result. At a timepoint t these are tuples. Again, we can concentrate on the tj and calculate the result sizes of left-overlap- and right-overlap joins as