MaxlHopitalApplications

How many times in all the rule may differentiate a quotient while one limit is being
computed. Bounding the depth alone does not bound the work: each step asks what the
two parts of its quotient tend to, and those are limits the rule may be applied to
in turn, so the steps fan out rather than follow one another, and sixteen deep is
far more than sixteen of them. This is a backstop rather than the answer to that --
the two conditions below are what keep the fan-out from starting.