3x3x2 (Domino)‎ > ‎

Roux 2x3x3

How to solve the Domino Roux style... 
First thing to to is to flip the puzzle around the z-axis so it has got 3x3 stickers on right and left sides and 2x3 in U, F, D, and B (resticker, it helps) then solve F2B and end in CLL, that is 16 cases including the solved one. And that will be all algs you need actually. But it helps to know the moves for solving the last pair of F2B, so also these cases are listed here (7+solved).
 
The moves; R, R', R2, L, L', L2, U2, F2, D2 and B2 are allowed turns. The last four may be notated without the "2" and only U, F, D and B may be used.
 
Last slot:

Corner and/or edge solved 
Solved 1:15
F corner 2:15
Was it lucky? [U2] L' D2 R U2 R' D2 R U2 (x')
B corner 2:15
Edge 2:15
R U2 R' U2 R U2 R' U2 R U2 R' R U2 L U2 R' U2 R U2 R' L'

Both pieces in U 
Paired 2:15
Blocked 2:15
[U2] R U2 R' R' U2 B2 L2 D2 L D2 L B2 (9,15)
Split F 2:15
Split B 2:15
R U2 R' U2 R U2 R' R L U2 R' U2 R U2 R' L'
 
CLL:

O cases
Solved 1:24
P parity 1:24
U2 in 50% of the cases R2 U2 R U2 R2 U2 R2 U2 R U2 R2
R2 U2 F2 R2 F2 U2 R2 F2 (8,16)
Diag R 1:24
Diag L 1:24
R2 U2 R' F2 U2 R2 F2 U2 R U2 F2 R2 F2 R' F2 L2 F2 U2 L U2 L2 U2 F2 L' U2 L2 U2 F2 L' F2

T cases
3-cycle R+ 1:12
3-cycle L- 1:12
R U2 L D2 L' U2 L D2 L2 (x') L' U2 R' D2 R U2 R' D2 R2 (x')
Op 1:12
Op and P 1:12
(x) U2 L2 U2 L U2 L' U2 L U2 L U2 R' U2 L U2 L' [U2] L2 U2 R' U2 L U2 L' U2 F2 L' F2 L' [U2]
 
U cases 
O parity 1:12
O and P 1:12
R' U2 R B2 U2 R2 U2 R' U2 B2 R2 B2 R B2 U2 R' (y2') F2 R2 F2 U2 R U2 R' U2 R2 F2 L F2 R' F2 R [F2]
3-cycle R- 1:12
3-cycle L+ 1:12
R L D2 L' U2 L D2 L' U2 R' L' R' D2 R U2 R' D2 R U2 L

H cases 
Checkers + 1:24
Checkers - 1:24
L U2 L2 U2 L' U2 L U2 L' U2 L2 U2 L [U2] R' U2 R2 U2 R U2 R' U2 R U2 R2 U2 R' [U2]
2-flip 1:24
2-flip and P 1:24
(L U2 R2 F2 R) U2 (R' F2 R2 U2 L') [U2] R' U2 L' D2 L U2 R L' U2 R' D2 R U2 L
 
Yep, it is the same cases as for pairing the last two edges using reduction on the 5x5x5. The algs you use for that will most likely also work for this method.