Is there an efficient algorithm that takes in a list of integer rectangle areas and finds all possible integer rectangle tilings?

For example, if we were given $$(2, 1, 2, 1, 1, 4, 1, 1, 6, 1, 1, 8, 1, 1, 10, 1, 1, 12, 1, 1, 14, 1, 1, 16, 1, 1, 18, 1, 1, 20, 1)$$

then one possible integer rectangle tiling is:

which uses the given list to tile a $11times 12$ rectangle.

So far, I’ve found What rectangles can a set of rectangles tile? on MO, and am trying to track down and adapt the references to my problem.

A similar but different problem is Filling rectangles with integer-sided squares.