Delay of an AND tree

should’nt the cost marked in yellow be big omega of log(n) (logn is the lower bound for the cost)?
becase an and tree cost is big theta of log(n) and maybe the inv will enlarge the delay.

also in slide 22 you state the the cost is big omega of log(n) for every decoder so just to be sure.

The AND tree is depth \log n. The inverted has costant delay.
Hence, the delay is O(\log n).
It is also \Theta(\log n).