Bill,
If I may, this is where we disagree, or where I believe we need clarification. I'll copy your post and highlight my suggestions in red.
Here goes:
Rule 44: Reopening the Bet
Example 1
This example demonstrates how multiple all-in bets, each to small to be considered a full raise over the most recent bet, can result in a full sized raise over an earlier bet.
Initial Action
NLHE with the blinds at 50-100. The following action occurs post flop:
Alice — opens with a min-bet of 100 and has chips behind
Bob — goes all-in for a total of 125
Charlie — calls the 125 and has chips behind (this is where I want you to state the required amount for a full raise if Charlie were to raise)
David — goes all-in for a total of 200 (the one and only player that raised Alice's bet 100%)
Erin -- calls 200 and has chips behind
Action Returns
When action returns to Alice, she is facing the 200 wager. Since her opening bet was 100, she is now facing a full raise of an additional 100. Therefore, betting is reopened for Alice who can now fold, call, or raise. (This is poker 101, but thank you for the explanation.)
Note, Bob’s raise was not a full raise over Alice’s bet. His raise (it's not a raise...it's a short all-in wager) to 125 only increased the current wager by 25. However, David’s raise to 200 is a full raise to Alice, but is not a full raise to either Bob or Charlie. Therefore, betting is reopened to Alice by virtue of David’s short all-in raise, the second such short all-in in this series. Notice, that when we are considering reopening the bet to Alice, there is no requirement for David’s raise to be a considered a full raise to any of the other players in the hand.
The following shows two additional options on how action might continue from this point.
Continuing the Action with Alice Calling
If Alice chooses to call the 200 by putting another 100 into the pot:
Charlie is now facing the 200 bet which is only a 75 raise over his previous 125 calling wager. Therefore, betting is not reopened to Charlie and he cannot raise. Charlie can either fold or call the 200 by putting another 75 into the pot.
Continuation with Alice Raising
If Alice raises all-in for an additional 150:
Charlie is now facing a wager of 250, which is a full raise of 125 over his previous wager. Therefore, betting is reopened to Charlie who can fold, call, or raise.
Summary
When a player, who has previously acted, is facing a full raise, betting is reopened and they may fold, call, or raise. Multiple all-in wagers, each to small to qualify as a full raise over the preceding bet, can result in a full raise over an earlier bet. (this multiple part is meaningless, lets put Bob all-in for 200...his single bet that doubled Alice's opening bet is what re-opens the betting, it has nothing to do with any combination or multiple all-in's from others. Your examples always are explained with an increase in all-in's...all-in for 14...all-in for 16...all-in for 19...if someone does not go all-in for at least 100% the betting is not re-opened. Period!)
In your example above, we have four possible situations that Charlie would face following Bob's all-in of 125.
a) Charlie may fold.
b) Charlie may call 125
c) Charlie may raise if he has enough which is a minimum of 100 more for a total of 225.
d) Charlie may go all-in for less than the required amount of 225. However, if his all-in wager totals 200 to 224, it will still re-open the betting to Alice because it is at least 100% of her opening bet!
That's it...if your still confused, or you think I've miss-stated something, I'd like to hear about it. Confusion stems from calling a short all-in a full raise when it is not. Alice bets 100, Bob all-in for 125, Charlie all-in for 201. Not really the required amount, UNLESS HE IS ALL_IN!!!!!