Can the President be Vice President?

So.. had a random call today that asked:

"If the Vice President runs for President and wins and nominates the former President as Vice President; if he then dies, can the former President legally be President again?"

(If Cheney rand for president, and picked Bush as his vice; and Cheney then dies, does Bush become President again?"

YES:
http://en.wikipedia.org/wiki/Vice_President_of_the_United_States

"The Twelfth Amendment to the United States Constitution requires vice presidents to meet the same requirements as presidents, and the 22nd amendment limits presidents to being elected to only two terms.

It is, however, debated whether a former two-term president could be elected Vice President since the 22nd amendment doesn't limit a president to serving two terms; it only prevents him from being elected to more than two terms. According to one interpretation a two term president could be elected to the vice-presidency and then serve another term in the presidency if the elected president died or was removed from office. The 22nd amendment only forbids election to, not service in, the presidency more than twice."

So the President can only be "elected" twice; he can serve as President the 3rd time because he was not "elected" into it, but secededd into it.