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This won't be fluid as you won't easily be able to easily see the FB. In addition, you may well have edges in the awkward places in FD/BD. As well as this, the movecount will be higher than just Roux F2B which I would consider to be better than ZZF2L as it has better lookahead becuas eyou don't have to blockbuild after a slightly jarring transition after EO.
No, ZZF2L, can be equally as efficitent as roux F2B, you just need to do more FMC stuff and blockbuild. also, the FD/BD problems are fixed by either putting a random U layer edge or by putting in UR and UL so after COLL its just M2 and 4c.
 
I had an interesting idea for a ZZ+ Roux mix.
this is to make the most fluid method ever, because ZZF2L is really fluid, but the Last layer is just as unfluid as CFOP.
I like roux's last steps, CMLL and LSE, but the blockbuilding is a little less fluid(lookahead is not as good as ZZF2L)

so what I did was this:
step 1:EOUnline- this is an EOline but with either A)2 U layer edges instead of line or B) place the UR/UR edges in the line instead, to make a really fast last steps
step 2:ZZF2L- because the line is a psuedoline this looks a lot more like F2B+EO, but treat it like ZZF2L.
step 3:COLL-Either influence into a shorter algset or use full COLL, either way, not too bad alg-wise.
step 4:finish with a kind of LSE-not really an LSE, but based on your EOUnline choices, it could be:
A)4b and 4c
B)do an M2 to solve UL/UR and then do 4c: because of how it starts, you can use BU recog right at this point, right after COLL.

maybe not good movecount wise, But I think that if we are looking for the most fluid method we combine the two most fluid things anyone has come up with yet: ZZF2L and LSE.
Can use improvement. IMO best first step is to solve EO and UR and UL, then place these edges as if they were the EO line. Then do ZZF2L into COLL, probably with some influence, then "resolve" UR/UL into L4E. I think this would best be approached as:
1. I solve with yellow on top at all times, to I would offset the cube by a X2, Z2 or M2 during inspection, then do EO line, which is actually just placing UR and UL at FD and BD.
2. ZZF2L
3. COLL, probably with some influence.
4. L4E
L4E is a little faster than EPLL because the case is always 3 moves (I think), and solving UL amd UR for good is only 3 moves max., equaling 6 moves which makes it faster than EPLLs, but not by a lot... Improvable.
 
I had an interesting idea for a ZZ+ Roux mix.
this is to make the most fluid method ever, because ZZF2L is really fluid, but the Last layer is just as unfluid as CFOP.
I like roux's last steps, CMLL and LSE, but the blockbuilding is a little less fluid(lookahead is not as good as ZZF2L)

so what I did was this:
step 1:EOUnline- this is an EOline but with either A)2 U layer edges instead of line or B) place the UR/UR edges in the line instead, to make a really fast last steps
step 2:ZZF2L- because the line is a psuedoline this looks a lot more like F2B+EO, but treat it like ZZF2L.
step 3:COLL-Either influence into a shorter algset or use full COLL, either way, not too bad alg-wise.
step 4:finish with a kind of LSE-not really an LSE, but based on your EOUnline choices, it could be:
A)4b and 4c
B)do an M2 to solve UL/UR and then do 4c: because of how it starts, you can use BU recog right at this point, right after COLL.

maybe not good movecount wise, But I think that if we are looking for the most fluid method we combine the two most fluid things anyone has come up with yet: ZZF2L and LSE.
I'd improve your method by doing this:
1. Normal EOLine
2. ZZ F2L
3. COLL
4. <M, U> EPLL
This is already one of the most popular ZZ variants.
 
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Can use improvement. IMO best first step is to solve EO and UR and UL, then place these edges as if they were the EO line. Then do ZZF2L into COLL, probably with some influence, then "resolve" UR/UL into L4E. I think this would best be approached as:
1. I solve with yellow on top at all times, to I would offset the cube by a X2, Z2 or M2 during inspection, then do EO line, which is actually just placing UR and UL at FD and BD.
2. ZZF2L
3. COLL, probably with some influence.
4. L4E
L4E is a little faster than EPLL because the case is always 3 moves (I think), and solving UL amd UR for good is only 3 moves max., equaling 6 moves which makes it faster than EPLLs, but not by a lot... Improvable.
yes.
 
Temp's TPLL Algorithms

What is TPLL?
TPLL is a method that I decided to make that allows you to permute both the first layer and the last layer simultaneously after solving the bottom cross incorrectly.

NOTE: I will edit this thread to add more algs whenever I have time.


Opposite Edge Swap on Bottom

Opposite Edge Swap


M2 U2 M2
This case is very easy to memorize and execute.


Adjacent Edge Swap

M2 U M U2 M U2 M2 U M2
(M2 U M') D2 (M U' M2) D2

The first algorithm isn't very fast, but the second algorithm feels awkward to execute. I would recommend the second case if you are good at fingertricking the D layer.​


W


M2 U M' U2 M U' M2
This case isn't too hard to learn, but executing it will take practice.


Oa


M' U M2 U M2 U M
This case is easy to learn, but executing it will be difficult for right-handed people. Each edge will rotate clockwise.


Ob


M U M2 U M2 U M'
This case is easy to learn, but executing it will be difficult for left-handed people. Each edge will rotate counter-clockwise.​
 
Temp's TPLL Algorithms

What is TPLL?
TPLL is a method that I decided to make that allows you to permute both the first layer and the last layer simultaneously after solving the bottom cross incorrectly.

NOTE: I will edit this thread to add more algs whenever I have time.


Opposite Edge Swap on Bottom

Opposite Edge Swap


M2 U2 M2
This case is very easy to memorize and execute.


Adjacent Edge Swap

M2 U M U2 M U2 M2 U M2
(M2 U M') D2 (M U' M2) D2

The first algorithm isn't very fast, but the second algorithm feels awkward to execute. I would recommend the second case if you are good at fingertricking the D layer.​


W


M2 U M' U2 M U' M2
This case isn't too hard to learn, but executing it will take practice.


Oa


M' U M2 U M2 U M
This case is easy to learn, but executing it will be difficult for right-handed people. Each edge will rotate clockwise.


Ob


M U M2 U M2 U M'
This case is easy to learn, but executing it will be difficult for left-handed people. Each edge will rotate counter-clockwise.​
Apart from the EPLL, almost all the other algs suck
 
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1. Orient all edges( EOLine minus the line)
2. Solve two opposite 1x2x3 blocks. This will be alot smoother due to the orientation of the edges.
3. Solve COLL
4. Last 6 edges

You get to skip step 4a in the last 6 edges due to the orientation of the edges.

What do yoi guys think?
 
on average, 4a takes about 5 moves.
the eoline would take more than that.
first block and second block will be less efficient if you want to keep orientation.
coll is worse than cmll.

the method won't be that bad, but would be clearly worse than regular roux.
 
Okay, very similar to CFOP...but an idea nonetheless. It's kinda like a method variation of CFOP
-Solve a cross on the bottom face.
The difference here is you don't need to worry about the way the edges are placed, so you can have an adjacent or opposite swap on the bottom.
-F2l
Same as CFOP
-OLL
Again same.
-PBCL?
Okay, since you have an edge swap on the bottom, the PLL will obviously be different. So I was thinking about generating a new set of PLLs for an opposite or adjacent swap on the bottom.

If you like learning more algs this could be an option...
If this was not ny idea please tell me!
 
While I'm no expert, it's easy for almost anyone to see that this method is fairly pointless.
You'd have to learn at least double the PLLs (recognition would probably also be pretty bad) to maybe save 1 or 2 moves for the cross. And considering the fact that it usually takes 6 or less moves to solve any cross, there's not much to be gained from this method.

If you like learning more algs, you should learn ZBLL or even give ZZ-CT a try.
 
While I'm no expert, it's easy for almost anyone to see that this method is fairly pointless.
You'd have to learn at least double the PLLs (recognition would probably also be pretty bad) to maybe save 1 or 2 moves for the cross. And considering the fact that it usually takes 6 or less moves to solve any cross, there's not much to be gained from this method.

If you like learning more algs, you should learn ZBLL or even give ZZ-CT a try.
I see your point.
Thanks for not being rude and stating your idea in a polite manner.
 
While I'm no expert, it's easy for almost anyone to see that this method is fairly pointless.
to maybe save 1 or 2 moves for the cross.

Actually it's not that obvious at all. If you assume that you saved 2 moves for the cross, it means that your lookahead during the 15 second inspection is significantly increased to the point where you would be able to build your first F2L pair in the inspection almost every time and some experts who can already do x-cross might even be able to build the 2nd pair during the inspection.


Eric Fattah
BC, Canada
 
That's a valid point, but cubers who are advanced enough to see first or even second pair (for easy cross solutions) during inspection are probably fast enough with CFOP that switching to this method wouldn't help very much. I think that becoming colour neutral (or just more practice) would be a better investment of time for them.
Also, this benefit will probably be negated by the last layer recognition. It would be the equivalent of learning full 4x4 PLL including parity (correct me if I'm wrong), which no one uses.
Another thing is that if you are completely free in the placement of cross edges, you could end up with an EPLL (U-perm, H-perm, Z-perm) on the bottom. How would you deal with those? You could do the regular PLL, followed by an x2 or z2, and then the EPLL or learn even more algs, neither of which is that great.

EDIT: Not full 4x4 PLL, only the adjacent and opposite edge swap cases.
 
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That's a valid point, but cubers who are advanced enough to see first or even second pair (for easy cross solutions) during inspection are probably fast enough with CFOP that switching to this method wouldn't help very much. I think that becoming colour neutral (or just more practice) would be a better investment of time for them.
Also, this benefit will probably be negated by the last layer recognition. It would be the equivalent of learning full 4x4 PLL including parity (correct me if I'm wrong), which no one uses.
Another thing is that if you are completely free in the placement of cross edges, you could end up with an EPLL (U-perm, H-perm, Z-perm) on the bottom. How would you deal with those? You could do the regular PLL, followed by an x2 or z2, and then the EPLL or learn even more algs, neither of which is that great.

EDIT: Not full 4x4 PLL, only the adjacent and opposite edge swap cases.

I like to leave 2 opposite edges swapped in cross if it's easier. If you can do some form of CP during OLL, then you'll end up with an EPLL, which can often result in a PLL skip if you do some setup moves and M2 U2 M2. If you can't do any CP, you can still sometimes force a better PLL case (e.g. getting a T-perm instead of an F-perm). Also, adding onto the actual method proposed, I feel like it wouldn't be that hard to learn recognition. We've already done it for normal PLL, and this is practically the same thing, but different cases. I think it's a pretty cool idea, but I'm not sure if it's worth the effort to learn all the algs.
 
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