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Since the start of the widespread adoption of CFOP in the early 2000s, the method has continually evolved and has reached a point where it goes beyond the initial steps. Top solvers no longer follow the rigid steps of Cross > 4 F2L pairs > OLL > PLL. More specifically, the FOP part of CFOP has evolved. There have been steps and techniques added to eliminate the O (OLL) in the FOP part of the name. Before OLL, the two most common are edge control and ZBLS. After OLL, and because of edge control or ZBLS, there is ZBLL. The F2L pairing step has also worked backwards to become incorporated into the cross through XCross or further.
This means that several methods have converged, and continue to do so. CFOP is no longer just CFOP. The method that is currently most commonly used by top solvers is a combination of CFOP, Petrus, and ZB if you consider ZB a separate method.
CFOP
Cross: CFOP, in its original steps, is obviously an evolution of the Layer By Layer method. Cross is most often the first step of Layer By Layer. The first known publication of the cross step is by Donald Taylor in 1978. It is possible that others were using the step even earlier, most likely in Hungary.
F2L pairs: This step has a complicated history. The first known publication of the idea is by John Conway, David Seal, and David Benson in 1979. This even included algorithms for every possible case. The idea was later independently discovered and published by several others. The most famous of these is its attribution to René Schoof in a 1981 issue of Cubism For Fun.
OLL + PLL: Two separate groups independently developed this idea in 1981. The first group is Hans Dockhorn and Anneke Treep, and the second is Jessica Fridrich and Mirek Goljan.
Pseudo Slotting: The first suggestion of this idea is by Olly Hayden. After putting the idea out there, it made its way to Chris Hardwick and Shotaro Makisumi, who both took an interest in the idea. This technique has seen much more frequent use in the past maybe five years.
Petrus
Let's start with XCross, XXCross, and beyond. Many of the top solvers are now planning and building one, two, or more pairs into the cross during inspection. Where does this idea come from? The origin of this can be seen in Petrus with its 2x2x3 step before finishing the F2L and then, before LL, almost always leaving a final F2L pair to solve. XCross and XXCross as a formal step for CFOP were proposed by Chris Hardwick from 2003 to 2004. Although everyone was aware of the Petrus method and block building, Hardwick's thought process likely wasn't to combine the two methods. It was instead likely a natural idea of combining the first one or two pairs with the cross step, using the well known block building technique.
Another major goal of a CFOP solve is to orient the last layer edges before arriving at the last layer. The two most common ways through which this is accomplished is edge control or ZBLS. Edge control, or orienting the edges during F2L, can first be seen in the Petrus method as one of the core steps. The step serves two primary functions: to make solving the rest of the F2L all RU gen and to reduce the number of last layer cases. The idea, in this case built around preserving the skeleton of the cross, eventually made its way to CFOP through Dan Knights and others. It came to be known as edge control in CFOP because the edge orientation is controlled during pair solving.
ZBLL is another major advancement. This step was developed for the Petrus method. Petrus designed the method to have an all edges oriented last layer. In the year 2000, Bernard Helmstetter singled out and specifically developed the algorithm set to be used for the Petrus method. A year or two later Zbigniew Zborowski and Ron van Bruchem proposed the ZB method which consists of the steps F2L-1 > ZBLS > ZBLL. However, Zborowski and Bruchem didn't independently re-propose the last layer step, nor did they develop the algorithms. On each of their websites they stated that the method is to solve F2L-1, use ZBLS, then to use Helmstetter's algorithms from the Petrus method. Unfortunately, because of the popularity of CFOP and the users' interest in the ZB method, CFOP users started calling the last layer step ZBLL to create a matching pair with ZBLS (then called ZBF2L).
Someone may argue that what differentiates the F2L of CFOP and Petrus is the solving of all four cross edges. However, one doesn't take precedence over the other. XCross and XXCross are the combination of the two independent ideas of Cross and Block Building. Cross being the core Layer By Layer step and Block Building being the Petrus invention. A similar argument may be put forth about edge control. CFOP orients edges throughout the F2L and Petrus does it at a specific point. But it is important to consider why CFOP has become less rigid. The method has had the major benefit of holding a massive number of users. This has allowed for many minds to experiment and put forth good ideas to evolve the method. Petrus didn't have that advantage and so it remains at its original rigid steps of 2x2x3 > EO > F2L > LL. If Petrus had gained many users in the early 2000s, the users would likely have evolved the method to include solving the final cross edge with the 2x2x3 while orienting all LL edges along the way. Even though this didn't get its chance to happen, the idea of orienting LL edges during F2L still remains originally proposed as part of the Petrus method.
Many in the community often ask "Why does no one use Petrus?" The answer is that they do. They use it every day and in every modern world record.
ZB
In the early 2000s Zbigniew Zborowski and Ron van Bruchem proposed the ZB method. The step of this method that makes it unique is ZBLS. Some around the time of the proposal had ambitions of learning the entire set, or even learned full ZBLS. However, it has taken a while for the step to catch on. In the past few years we have seen an increase in its use and it will likely continue to grow.
Summary: Name and Attribution
With the method having evolved beyond the original steps, does it make sense to continue to call it CFOP? If not, what should it be called?
In order to properly credit those who have contributed the primary steps and techniques, they are shown below. With some recent top solves involving orienting all edges at the start of the solve, maybe the ZZ method will be added to the bubble. Jake Williams (Swagrid) once created a video covering current top solvers incorporating EO during inspection. This would make for a convergence of four methods being what is currently used most often by the best solvers. What other steps or techniques may we see incorporated in the future? There is an interesting class of methods that do 3D block building after a 1x2x3 block, then solve the majority or all of F2L. The timeline of these is something like MI1 > Nautilus > CEOR > LEOR > Mehta > Squall > APB. Will anything from those eventually be incorporated, such as LXS, or early corner permutation to end in 2GLL instead of ZBLL? Or will those methods remain in their own class, converging into something of its own?
Cross
Donald Taylor (first known proposal)
F2L pairing
John Conway, David Seal, and David Benson: First known publication (1979).
René Schoof: First popular publication (1981).
Other small publications.
EO during F2L
Lars Petrus (Petrus method)
Dan Knights and others (edge control)
Zbigniew Zborowski and Ron van Bruchem (ZBLS)
XCross and XXCross
Lars Petrus (Petrus method block building)
Chris Hardwick (proposal for CFOP)
Pseudoslotting
Olly Hayden
OLL + PLL
Hans Dockhorn and Anneke Treep (1981)
Jessica Fridrich and Mirek Goljan (1981)
ZBLL
Lars Petrus: Designed the first speedsolving method that reduces to an all edges oriented last layer.
Bernard Helmstetter: Generated the algorithms for the Petrus method one look last layer.
Credit
This is an extension of Joseph Tudor's thread about method convergence. This one by me specifically focuses on what makes up what we currently call CFOP.
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