Re: Looking for a program that can...
the only programs I know of that can do this are your standard Traktor and Ableton types. As far as BPM detection goes anyways... Audacity is free and can handle stretching and saving to your format of choice, there may be a BPM detection plugin you can find for it but I don't believe one comes with it stock. Although you have protools listed in your icons there; does that not have some for m of timestretch? or are you just more interested in finding a standalone app to use and not have to boot up protools?
Either way, maybe poke around and see if there are any free BPM detection plugs you can find for audacity, if not hopefully someone else will know exactly the program you're looking to find.