I am looking for an algorithm which can compute the time required to reach the full stage of trellis. I understand that it has to be a function of channel memory, length of input at any given time.

For example
channel memory=2
length(input)=1

then at any time index and any given stage we can reach to 2 states out of 4 states. So we need at least two time hops to be able to reach ANY state in the trellis.

but if
channel memory =2
length(input)=2

then any state can be reached in just one time hop.

Do we have any such algorithm which can compute min(time) required .