First layer

A face with its permutation.
The 2x2 has only corners. Every method starts with one side: a face (four stickers of one colour) or a layer (a face with its side colours matching). Then:
  • •
    Ortega: a face, then orient the opposite face (7 OLLs), then permute both layers at once (6 PBLs): 13 algorithms.
  • •
    CLL: a full first layer, then one algorithm for the whole last layer (40). Fewer looks; the first layer costs a few more moves.
  • •
    EG: a face only, then one algorithm that also fixes the bottom's permutation: CLL (bottom solved), EG-1 (adjacent swap below) and EG-2 (diagonal swap below), 120 algorithms. The top method for competition.
A first face done; the top is an Ortega OLL case (Antisune).
Checked by the engine: Ortega OLL Anti Sune
R U R' U R U2 R'
Both faces done: one PBL left (an adjacent swap on top).
Checked by the engine: PBL Adj
R U R' U' R' F R2 U' R' U' R U R' F'

Ortega OLL

7 cases · Orient the 2x2's top face over a solved bottom face: 7 cases.

PBL

6 cases · Permute both layers of a 2x2 at once: 6 cases.

CLL

40 cases · Solve the 2x2's last layer in one algorithm after the first layer: 40 cases.

EG-1

40 cases · Solve a 2x2 whose first face has an adjacent corner swap underneath: 40 cases.

EG-2

40 cases · Solve a 2x2 whose first face has a diagonal corner swap underneath: 40 cases.