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^{Note: since asking this question I've purchased several other twisty puzzles and now regret taking the "look up algorithms online" approach to solving - in the end I get much more enjoyment from the puzzles where I worked out to solve them myself than the ones where I didn't. If you're stuck at this point I would recommend seeking resources to understand the concept of parity and then try to come up with a solution yourself. You won't end up with a super efficient algorithm, but you will understand it, which is ultimately more satisfying. Or it is for me at least. That said, answers to this question are still welcome.}

I'm solving my 4x4 Rubik's cube (aka Rubik's revenge) for the first time, and I have the "OLL parity" case:

There are plenty of algorithms for this available online, but different people use different notation and nobody ever says which one they're using, so I risk messing up my cube if I guess wrongly.

So, please give me algorithms for solving the OLL parity, using the following notation:

• 
  R: turn just the rightmost face clockwise


• 
  Rw (R wide): turn the rightmost half of the cube clockwise, i.e. the rightmost face and the slice adjacent to it


• 
  r: turn the rightmost slice clockwise, but not the rightmost face


• 
  R2, Rw2, r2: as above but turning it twice


• 
  R', Rw', r': as above but turning it anticlockwise


• 
  L, F, B, U, D: left, front, back, up, down. (All clockwise by default, can be modified as above)


• 
  x: if you use this, please explain what it means, as I have no clue.


• 
  - (hyphen): if you use this, please explain what it means, as I have no clue.


• 
  (, ) (parentheses): if you use these, please explain what they mean, as I have no clue.

If you use anything else at all in your notation, please explain what it means. If you prefer a different notation from the above that's fine, but please explain it.

I'm holding my cube with the unsolved cubies facing me at the top. (i.e. the red face would be the front in the diagram above.) If I should start in some other orientation, please say so.

It would be helpful to have an algorithm that leaves all other pieces alone, as my cube is in exactly the almost-solved state above. But if algorithms that don't do this are significantly shorter and/or easier to remember then that would be fine too. (Please tell me which I can expect in your answer!)

Here is the algorithm I use (from http://www.rubiksplace.com/cubes/4x4/), but using your notation:

Rw U2 x Rw U2 Rw U2 Rw' U2 Lw U2 Rw' U2 Rw U2 Rw' U2 Rw'

So it's basically a bunch of half cube turns and top face 180 degree turns.

The "x" means you rotate the cube clockwise along the x-axis. In other words, if the Red face was facing you, it will move to the top while the sides stay the same color.

I use the following that leaves all the other cubes alone:

r U2 r U2 r' U2 r U2 l' U2 r U2 r' U2 lr' r' U2 r'

If you look at it this way, the net effect is just an r' :

r U2 r

U2 r' U2 r U2 l'

U2 r U2 r' U2 l

r'

r' U2 r'

Not technically an answer, but here is the meaning of the symbols:

x, y, z :

These are notation for rotation of the entire cube. they mean to rotate following the R, U, and F moves, respectively.

-: I don't know what the hyphen means. Can you tell me where you saw the hyphen?

( )

! These don't change what to do, they just tell you what moves are triggers, or sets of moves that repeat through many algorithms.
You usually see them around sets of moves like (R U R' U') (R' F R F') and (R U2 R')