Password Similarity Check

Question

To keep people from switching to a password that is barely different, a company compares each new password with the one it replaces. The pair is similar if you can edit the new password so that the old one shows up in it as a subsequence. The only edit allowed is to shift characters forward: for as many positions of the new password as you like, swap the letter for the next cyclic character of the alphabet, so 'm' turns into 'n', 'q' into 'r', and 'z' wraps around to 'a'. ...