Lt-UnReaL already corrected the U->U' error in your message.Take a look at all those algs again. the actual move is just (R U R'). The F' is just a setup or an undo setup.
From your example:
F (RU'R'U') (RUR'F') (RUR'U') (R'FRF').
F (RUR'U') (RUR') F' (RUR'U') (R'FRF')
You can easily deduct this by seeing that all those (aba'b') moves actually cancel to nothing (a - a' = nothing) or at most an AUF.