dec 0 d 0 dec x 0 x dec s x s d dec x d grec 0 d U F U grec s x s d U F grec dec x d s d F U x F sumlog x grec x s s 0 0 z1 nat z2 nat + log2 s z2 0 z1 + 0 x x + s x y s + x y log2 s 0 0 0 log2 0 s y s log2 s y 0 log2 s 0 s y s log2 s y 0 log2 s s x y log2 x s y d nat x nat y nat U nat F nat nat nat 0 nat s nat nat dec nat nat nat grec nat nat nat nat nat nat nat sumlog nat nat + nat nat nat log2 nat nat nat FULL .