ZZ

EOLine, then a rotationless F2L with R, U and L, then a last layer that always has a cross.
ZZ (Zbigniew Zborowski, 2006) orients every edge first. After that, F and B turns are never needed: F2L is built with R, U and L only, which is fast to turn and needs no rotations, and the last layer always arrives with its edges oriented.
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    EOLine: orient all 12 edges and place the DF and DB edges (about 6 moves).
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    F2L: build the left and right 1x2x3 blocks around the line with R, U, L.
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    Last layer: OCLL + PLL (2-look), COLL + EPLL, or ZBLL (one look, 493 cases).
An EOLine state: every edge oriented, the DF-DB line placed.
R U L' U2 R2 L U' R' U
ZBLL is ZZ's endgame: seven subsets of 72 cases (H has 40) named by corner orientation. Most ZZ solvers learn COLL first, then ZBLL subset by subset, starting with T and U.