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Hi, I'm Nathan.
Sorry to hear that you're having trouble with this but I'll do my best to help you.
Unfortunately your tivo system will not integrate well with the new cox systems. A box will be required, but the mini box usually isn't sufficient. You may be better off getting the full size box, and then you'll need to go into your tivo menu and program it to operate the new cable box, via an IR emitter that will sit in front of the box. This lets the tivo control the channels on the box. It will be limited to 1 program at a time.
Since you have older model equipment, you would probably be better off retiring the tivo at this point and just getting a DVR provided by cox. You'll get better picture quality and far more storage space, with everything consolidated into a single remote.
Best regards, ***** ***** for the news,
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