Understanding an example of LZW decompression algorithm

Question

I'm trying to understand this example of decompression using the LZW algorithm.

I would like to undestand why we insert ba in row 4; we're currently at i=3, so the index s=ab as shown in row 3; we previously had a and b so aren't we supposed to look for abab in the dictionary? So why is the result ba and not abba?

Answer 1

From the English version of Wikipedia: "Buffer input characters in a sequence ω until ω + next character is not in the dictionary. Emit the code for ω, and add ω + next character to the dictionary. Start buffering again with the next character."