I would like to mention that it may be somewhat ambiguous what is meant by "resolving algs." You might or might not mean the same thing as the order of the alg (as defined by group theory).
The move x has order 4 even though (assuming you start from a solved cube) the cube remains solved after each time x is applied.
Also, 4x4x4 and larger cubes have indistinguishable centers that allow non-identities to seem like identities. For example (with lower case letters meaning single layer turns - the layer next to the face layer) , f' r' u' r U r' u r U' f has order 3 even though applied to a solved cube, it returns the cube to the solved state (unless it's a supercube). If you take a solved cube, and apply the move b before applying f' r' u' r U r' u r U' f, you see that the cube doesn't return to the same state you had before applying f' r' u' r U r' u r U' f.
It's also possible to reach an identity somewhere in the middle of one of the applications of the alg. A rather trivial example of this is R2 U2 R2 U2 R2 U2 R2 U2 which has order 3, but reaches an identity after one and a half times.
The following link (
http://www.geocities.com/jaapsch/puzzles/cubic3.htm#p34 ) gives the list of all the possible orders for positions in the <U,D,L,R,F,B> group (and how many of each). I wonder if someone has calculated all the possible orders for the <U,D,L,R,F,B,M,E,S> group (aka <U,x,y> group).