Bob Hyrule writes his own name in the death note:
Bob Hyrule, peaceful heart attack. Dies peacefully from a heart attack in 20 days.
So let's say, he then decides to make the Shinigami eye deal. Can he make the Shinigami eye deal? If yes, will he die in 10 days, because he gave his remaining lifespan, or will he still live 20 days?