¹²As a simple (and only approximative) numerical example, think of dividing a tree of length 20 into two parts. Each part of length 10 has 1, 024 = 2¹⁰ states, so the two search trees have total of 2, 048 states. This is much less that the original tree with 2²⁰ = 1, 048, 576 states.