I suspect trying to reductively understand intelligence is a bit like trying to reductively understand biology - every level of abstraction is causally influenced by every other level of abstraction, so there just aren't simple primitives you can break everything down into.
Trying to express the high-level behaviour of an organism in those reductive terms is way beyond science right now, if it's even possible at all. Like have a look at a chart of human metabolic pathways - it's absolute insanity. And those are extremely simplified already!
