I was wondering if it's possible to solve a Rubik's cube just iterating a single algorithm. It doesn't matter how complex the algorithm is (as long as it is less than 1 million moves), nor the time required to solve the cube; I just want to know if there exists a "periodic" sequence of moves that allows to turn any valid scrambled configuration to the solved configuration. Once you start executing the algorithm, you can't stop it (unless you finish, of course), rotate the cube and start it on another face.
If the question is still unclear, let's make an example. You have to find a sequence like this one, to be repeated an unlimited number of times, that lets you solve any configuration:
Example: U D R' U' F L' U F' R' U' L D' R to be repeated 12412183213 times!
Note: The above sequence is just an example, 99,999% it's not working!
I just ask you to prove whether such sequence exists or not. If it exists, I would appreciate you to post it, unless it consists of more than 1000 moves.