I'm working through a proof that is a simplified version of David Maeirs LCS reduction from the VERTEX-COVER problem and I had a question about a specific set of instructions and how to execute them by hand.
The part I don't understand of the proof
Now I think this would imply that I need to line up S0-S7 vertically and using that rule show I can find the LCS, which was shown in my proof to be
I tried doing that but was unable after many attempts to show that I could in fact induce $Topt$ from the sequences below. Could someone explain where I'm going wrong here? Did I misinterpret the instructions?
EDIT: I tried everything I could think of to see if I could make any of them work but didn't think it was relevant enough to include, if you want to know what I did I can list them.