Merely looking at the written solve, the one thing that stands out immediately is that the solutions are

1. This scramble has no pre-made pairs at all, so it's not clear which colours one should use to build the initial 222 block. I see that the blue-yellow-red corner can join with either the blue-yellow edge or the red-yellow edge in one move, and there's also two correctly permuted cross edges on the blue face. Try for example:

x L2 // corner-edge pair

(U' D') // two 2×2×1 blocks

R' // join the blocks to get a 2×2×2

2. L' U' // edge

Two moves for a single edge is very inefficient, considering there are already multiple free/1-move edges all over the cube. Make use of edge-centre pairs when they show up (and they show up very often), but don't go out of your way to make them. Also, since you're following this up with a z2 rotation, you can also rotate first, executing it as z2 R' D' instead.

3. It looks like you're trying to solve the 222 block by doing a half-cross and then inserting an F2L pair.

F U' F' R U' R2 U' R' // insert white-orange

F' U' F U2 F' U F // white-green-orange F2L slot

Don't do this. (I don't know how to solve this specific situation well either, but I wouldn't have chosen this block anyway. Herein lies a strength of Petrus and other blockbuilding methods: you don't have to know how to solve

4.

y' F2 // white-red edge

L2 U L' U' R U R' // white-red-green F2L slot

Again, a CFOP-y approach, but here I don't see anything else obvious so this is acceptable.

5.

y2 U F' U' F R2 U2 F' U' F // EO

I would've just done a y' rotation, so that edge orientation can be done with R U* R' / L' U* L / R' F* R / L F* L' triggers, which are better than F' U* F and B U* B' triggers. Anyway, this EO case can be done in 5 moves:

y2 F R2 F2 U F

The five-move solution is very awkward to execute from this angle (orange in front), but if you'd done a y' rotation instead of a y2, it'd be like this:

y' Rw U2 Rw2 F Rw

Way better. I think you mostly just need to familiarise yourself with how to fix bad edges, because it looks like you're using only F' U' F to flip the UL and FR edges, when there are many other ways to flip two edges.

6.

U' R2 U R2 U' R U' R' U R // white-red-blue F2L slot

U R U R' U2 R U R' // white-orange-blue F2L slot

Not sure what the initial U' is for. I guess you were trying to influence the next slot, which isn't a bad idea in general, although this is pretty tricky and in this specific case, it just replaced a 7-move last slot case with another 7-move last slot case. Other than the initial U', this is fine, although you can also look at other ways to solve a square on the right face, e.g.

R' U' R' U2 R' U' R2 // white-orange-blue square, then

R U2 R2 U' R2 U' R' // white-red-blue slot

7.

y' F U R U' R' U R U2 R' U' R U R' F' // COLL (you typoed the rotation)

U M2 U' M U2 M' U' M2 U // EPLL

Do not

*very*long. I normally expect each line/step to be 5-10 moves, with the exception of last layer algs. Point by point breakdown, starting from the scramble. Blue text indicates your solve, red text indicates my suggestions.1. This scramble has no pre-made pairs at all, so it's not clear which colours one should use to build the initial 222 block. I see that the blue-yellow-red corner can join with either the blue-yellow edge or the red-yellow edge in one move, and there's also two correctly permuted cross edges on the blue face. Try for example:

x L2 // corner-edge pair

(U' D') // two 2×2×1 blocks

R' // join the blocks to get a 2×2×2

2. L' U' // edge

Two moves for a single edge is very inefficient, considering there are already multiple free/1-move edges all over the cube. Make use of edge-centre pairs when they show up (and they show up very often), but don't go out of your way to make them. Also, since you're following this up with a z2 rotation, you can also rotate first, executing it as z2 R' D' instead.

3. It looks like you're trying to solve the 222 block by doing a half-cross and then inserting an F2L pair.

F U' F' R U' R2 U' R' // insert white-orange

F' U' F U2 F' U F // white-green-orange F2L slot

Don't do this. (I don't know how to solve this specific situation well either, but I wouldn't have chosen this block anyway. Herein lies a strength of Petrus and other blockbuilding methods: you don't have to know how to solve

*every*situation well, because 99% of the time you can just choose a different, easier starting block.) Even if you wanted to do it half-cross-then-slot, it would've been better to rotate to solve the F2L slot rather than use so many F moves in succession.4.

y' F2 // white-red edge

L2 U L' U' R U R' // white-red-green F2L slot

Again, a CFOP-y approach, but here I don't see anything else obvious so this is acceptable.

5.

y2 U F' U' F R2 U2 F' U' F // EO

I would've just done a y' rotation, so that edge orientation can be done with R U* R' / L' U* L / R' F* R / L F* L' triggers, which are better than F' U* F and B U* B' triggers. Anyway, this EO case can be done in 5 moves:

y2 F R2 F2 U F

The five-move solution is very awkward to execute from this angle (orange in front), but if you'd done a y' rotation instead of a y2, it'd be like this:

y' Rw U2 Rw2 F Rw

Way better. I think you mostly just need to familiarise yourself with how to fix bad edges, because it looks like you're using only F' U' F to flip the UL and FR edges, when there are many other ways to flip two edges.

6.

U' R2 U R2 U' R U' R' U R // white-red-blue F2L slot

U R U R' U2 R U R' // white-orange-blue F2L slot

Not sure what the initial U' is for. I guess you were trying to influence the next slot, which isn't a bad idea in general, although this is pretty tricky and in this specific case, it just replaced a 7-move last slot case with another 7-move last slot case. Other than the initial U', this is fine, although you can also look at other ways to solve a square on the right face, e.g.

R' U' R' U2 R' U' R2 // white-orange-blue square, then

R U2 R2 U' R2 U' R' // white-red-blue slot

7.

y' F U R U' R' U R U2 R' U' R U R' F' // COLL (you typoed the rotation)

U M2 U' M U2 M' U' M2 U // EPLL

Do not

*ever*do y rotations during the last layer. Rotations are a lot slower than AUFing. Other than that, this is fine, although I'm a bit concerned about why you know COLL when you're still having trouble with general efficiency.
Last edited: Jul 2, 2018