Suppose we could solve the Rubiks cube(final steps) by using the operation $[R',D']$ a certain number of times where square brackets denote commutator operation. Then, would $[D', R']$ reduce the number of steps required?
I think yes, but am not able to reach the proof. Does the cycle decomposition of $R,D$ have a role to play here? And the commin support of $R,D$? Thanks beforehand.