Operation counts (counted, not timed)
=====================================

nextGreater on a strictly decreasing array (the worst case for the scan-right version)
       n scan-right compares     stack compares stack push+pop
    1000             499500                999           1000
   10000           49995000               9999          10000
  100000         4999950000              99999         100000

nextGreater on random values (n = 100000): every index is pushed once and popped at most once
pushes = 100000, pops = 99985, comparisons = 199977  (bound: comparisons <= 2n = 200000)

QueueViaStacks: n enqueues followed by n dequeues
       n    total element moves moves in the 1st dequeue
    1000                   1000                     1000
   10000                  10000                    10000
  100000                 100000                   100000
one dequeue can cost n moves, but each element moves exactly once, so n enqueues + n dequeues cost 3n steps in all

StackViaQueue: n pushes
       n      total rotations       n(n-1)/2
     100                 4950           4950
    1000               499500         499500
    5000             12497500       12497500