We are looking for an alg to describe U' in terms of U, D, R, L, F, B, i.e., clockwise quarter turns without repetition and each turn can not be followed by the opposite layer. Note. If we can do that for U', we can also do it for any other layer by transposing the turns.

2. Secondly, perhaps it's easier if we allowed half turns as well.

3. Thirdly, if opposite turns are allowed, we are not allowing the a pair of opposite turns to be repeated more than twice, otherwise, we'd get U' = D (U D)3.

Can anybody help?