[tsimionescu]

You personally reverse engineering an app on your phone has been quite well established as legal.

You releasing a competing product after having personally worked on reverse engineering someone's product is a lot murkier, and easily opens you up to copyright lawsuits, which you'll have a hard time fighting if you do happen to have similar code, since in copyright it matters not just if the code was similar, but also whether it's likely that you actually copied it (unlike patent law).

This can and has been done, but normally you want a very clear firewall between the reverse engineering team and the dev team, with lots of paperwork proving that no-one on the dev team ever saw a line of code from the reverse engineering team - they were only told concepts and ideas, which are not copyrightable. This is how the first free Unix was created, for example.