You have a string of bits. You scan from right to left.
If you encounter a '1', you have the option to flip it to a 0 or keep it as is.
If you encounter a '0', your adversary has the option to flip it to a 1 or keep it as is.
Your goal is to zero all the bits once you reach the end of a scan (i.e. at the left most bit), whilst you adversary wishes to prolong the game indefinitely.
We continually re-scan until we reach the aforementioned goal state.
Can you prove that the game will eventually terminate?