They couldn't leave the other one alive it was impossible. They were both "traitors" in each other's proclamations and both had too much influence to remain alive. Most likely if one captured the other they would have the other one commit an honorable suicide. There would be no way at least in my mind that one would trust the other to live and not betray them.
"If you can't drink a lobbyist's whiskey, take his money, sleep with his women and still vote against him in the morning, you don't belong in politics."