Step 4:  PLL

This section is currently a nearly direct copy of the PLL page formerly on Jason Baum's website. Since his site is down, I'm rehosting his algorithms here, and in due time I intend on including all optimal algorithms for each PLL from each angle. ~Ranzha

Step 4 of this method is permutation of the last layer, Square-1 style.  This should be very straightforward if you are comfortable with regular PLL.  Recognition is essentially the same on Square-1, though the angles are sometimes different.  For example, on the G perms, instead of putting the side with the matching corners on the left, you are going put them on the right and look for your block from there.  Also keep in mind that because of the way Square-1 works, you will not always be able to "line up" the alg before you start it, so you will most likely have to AUF to finish the solve.

Because parity exists on Square-1, there are 43 PLLs in this step (21 without parity, 22 with parity).

Special thanks to Henrik Aagaard and Maarten Smit, who kindly generated the majority of the PLL cases with parity!

Without Parity:
Ua (1,0) / (0,-3) / (-1,0) / (3,0) / (1,0) / (0,3) / (-1,0) / (-3,0) /
[8|16]
Ub / (3,0) / (1,0) / (0,-3) / (-1,0) / (-3,0) / (1,0) / (0,3) / (-1,0)
[8|16]
H / (3,-3) / (3,-3) / (0,1) / (-3,3) / (-3,3) / (-1,0)
[6|16]
Z / (3,3) / (0,3) / (1,1) / (-1,-4) / (-3,-3) /
[6|15]
Ab / (0,-3) / (-2,0) / (3,0) / (2,0) / (0,3) / (-2,0) / (-3,0) / (2,0)
[8|16]
Aa (-2,0) / (3,0) / (2,0) / (0,-3) / (-2,0) / (-3,0) / (2,0) / (0,3) /
[8|17]
E / (3,3) / (1,-2) / (2,2) / (-3,0) / (-3,-3) /
[6|15]
J / (3,0) / (0,-3) / (3,0) / (-3,0) / (-3,3) / (-3,0)
[6|13]
L (1,0) / (3,0) / (0,-3) / (3,0) / (-3,0) / (-3,3) / (-4,0)
[6|14]
Rb (1,0) / (3,0) / (-3,0) / (3,0) / (0,3) / (2,5) / (1,4) / (3,3) / (2,0)
[8|20]
Ra / (3,3) / (1,-2) / (-4,-1) / (0,3) / (3,0) / (-3,0) / (3,0) / (0,-3)
[8|19]
T / (0,3) / (3,3) / (0,3) / (4,0) / (3,0) / (3,3) / (3,0) / (5,0)
[8|18]
F (-2,0) / (-1,-1) / (-3,0) / (3,0) / (1,4) / (-3,0) / (3,0) / (2,-4) / (-3,0) / (0,1)
[9|22]
Y (1,0) / (3,0) / (3,3) / (3,0) / (5,0) / (0,3) / (3,3) / (0,3) / (3,0)
[8|19]
V (1,0) / (2,2) / (3,0) / (0,-3) / (4,1) / (3,0) / (-3,0) / (5,-1) / (0,3) / (0,-2)
[9|22]
(-3,0) / (3,0) / (-3,-3) / (0,3) / (0,-4) / (1,-5) / (0,3) / (-1,2) / (3,0) / (-3,0) / (0,-5)
[10|24]
Gd / (3,3) / (1,4) / (2,-1) / (3,0) / (-3,-3) / (0,-3) / (0,-3)
[7|18]
Gc / (-3,0) / (3,3) / (3,0) / (1,-2) / (-1,2) / (-3,-3) / (-3,0)
[7|18]
Gb (1,0) / (0,3) / (0,-3) / (0,3) / (0,-3) / (2,0) / (-3,3) / (3,-3) /
[8|18]
Ga / (-3,3) / (3,-3) / (-2,0) / (0,3) / (0,-3) / (0,3) / (0,-3) / (-1,0)
[8|18]
Na / (3,3) / (3,0) / (3,3) / (3,0) / (3,3) / (3,0)
[6|15]
Nb (1,0) / (3,3) / (3,0) / (3,3) / (3,0) / (3,3) / (2,0)
[6|16]

With Parity:
Edge Slash (0,-3) / (-3,0) / (0,-1) / (0,4) / (3,2) / (0,-3) / (-5,4) / (0,4) / (0,-4) / (2,-2) / (0,5) / (3,3) /
[12|28]
Edge I / (3,3) / (-1,0) / (2,-4) / (4,-2) / (0,-2) / (-4,2) / (1,-5) / (3,0) / (3,3) / (3,0)
[10|26]
Oa / (3,3) / (1,0) / (-2,-2) / (2,0) / (2,2) / (-1,0) / (-3,-3) / (0,2) / (-2,-2) / (-1,0)
[10|25]
Ob (1,0) / (2,2) / (0,-2) / (3,3) / (1,0) / (4,4) / (0,-2) / (2,2) / (0,-1) / (3,3) /
[10|25]
W (4,3) / (2,-4) / (-5,0) / (0,-3) / (-1,0) / (0,-4) / (0,4) / (4,0) / (2,3) / (0,-3) / (-4,0) / (0,3) /
[12|27]
Corner Slash (3,-4) / (4,-2) / (2,-4) / (1,0) / (3,3) / (4,-3) / (4,-2) / (2,-4) / (0,5) / (-3,-3) /
[10|28]
Corner I / (3,3) / (3,0) / (2,-4) / (0,-4) / (4,-2) / (2,-4) / (4,6) / (1,-2) / (-3,-3) /
[10|26]
Mi / (3,3) / (1,-4) / (4,-2) / (2,-4) / (2,0) / (-2,4) / (1,-5) / (-3,0) / (3,3) /
[10|26]
Ki / (3,3) / (1,-4) / (4,-2) / (2,-4) / (-4,0) / (-2,4) / (1,-5) / (3,0) / (3,3) /
[10|26]
X / (3,3) / (5,2) / (-4,2) / (2,4) / (-4,2) / (4,-2) / (0,4) / (0,3) / (3,3) / (6,6)
[10|27]
Ka / (3,3) / (5,2) / (2,-4) / (4,0) / (4,-2) / (2,-4) / (5,-5) / (0,-3) / (-3,-3) /
[10|26]
/ (3,3) / (5,2) / (2,-4) / (-2,0) / (4,-2) / (2,-4) / (5,1) / (0,-3) / (-3,-3) /
[10|26]
Qb (4,0) / (3,-1) / (3,0) / (-3,0) / (5,-5) / (-4,0) / (4,-4) / (0,-4) / (-4,0) / (0,-2) / (-1,0) / (-3,0) /
[12|27]
Qa (4,5) / (0,3) / (-4,0) / (0,-3) / (0,-5) / (-4,-4) / (0,-4) / (4,0) / (-2,0) / (0,5) / (-3,0) / (0,1) / (-1,0)
[12|27]
9a / (3,0) / (1,0) / (-2,0) / (-4,0) / (0,-4) / (-5,2) / (0,-1) / (0,-3) / (0,4) / (5,2) / (-2,4) / (2,0)
[12|27]
9b (-2,0) / (2,-4) / (1,4) / (-4,0) / (0,3) / (1,0) / (-1,4) / (0,4) / (4,0) / (2,0) / (-1,0) / (-3,0) /
[12|27]
Ωa (3,0) / (-3,0) / (-2,0) / (5,3) / (2,-1) / (-4,0) / (4,0) / (2,-5) / (0,3) / (-5,0) / (0,3) / (0,3) / (2,0)
[12|28]
Ωb (4,0) / (3,2) / (3,0) / (0,-5) / (3,0) / (-1,0) / (-4,0) / (0,4) / (-2,1) / (-3,-5) / (2,0) / (0,3) / (3,0)
[12|28]
Pa (3,0) / (0,3) / (-3,3) / (2,1) / (0,-2) / (2,0) / (-4,0) / (0,2) / (0,-2) / (0,1) / (0,-3) / (0,-3) /
[12|26]
Pb (0,6) / (0,-3) / (0,-3) / (0,-4) / (0,2) / (0,-2) / (4,0) / (-2,0) / (0,2) / (1,-4) / (0,3) / (-3,3) /
[12|26]
αa / (3,3) / (-1,0) / (0,-4) / (-5,0) / (-3,0) / (1,0) / (0,4) / (0,-4) / (5,-2) / (0,-3) / (-3,3) /
[12|26]
αb (-3,0) / (-3,0) / (4,-1) / (0,-2) / (0,2) / (-4,0) / (2,0) / (0,-2) / (1,0) / (-3,0) / (-3,3) / (3,0) /
[12|26]