CxLL Recognition Systems

This is my attempt at organizing the various CxLL recognition systems. Obviously because every piece has an orientation and a permutation, it could be simplified to saying that everything is checking a separate orientation and permutation. But it's more complicated than that and classifying that way doesn't reflect how some recognition systems work in solve. For example, NMCxLL 2 and ATCRM have permutation information built into their specific type of inital orientation check. Another example is that the four sticker Straughan recognition is one step and not determined by thinking about the four stickers' separate orientations and permutations. Some systems are also hybrids, such as ATCRM or the positional version of Straughan.

Looking through these, new systems can be imagined by combining, or filling in the gaps where a recognition style should exist. New ZBLL, 1LLL, and other step recognition systems have been made based on the CxLL systems.

Orientation > Pattern

Waterman

Orientation then 3-4 sticker pattern

Marc Waterman and Daan Krammer (1981)

Setup: U2 R U2 R' U' R U' R'

Intuitive

Orientation then side sticker order

First known mention by Michael James Straughan (2006)

Setup: U2 R U2 R' U' R U' R'

1-Side Sune

Orientation then 3 stickers on U

Spencer Schumann (2020), Ryan Hudgens (2024)

Setup: U2 R U2 R' U' R U' R'

NMCxLL 2

LR Orientation then predetermined location pattern

Michael James Straughan (2010)

Setup: R U R' U R U2 R'

ATCRM

LR Orientation then two stickers

Michael James Straughan and Tim Mosher (2021)

Setup: R U R' U R U2 R'

Straughan (positional, minimum pieces)

Orientation then pattern, using just visible stickers of UFL, UFR, and UBR

Michael James Straughan (2026)

Setup: F U R U' R' U R U' R' F'

Straughan + ATCRM hybrid

LR or FB orientation then two stickers, within UFL, UFR, and UBR

Michael James Straughan (2026)

Setup: R U R' U R U2 R'

Orientation > Orientation

NMCxLL

LR or FB orientation then U orientation

Gilles Roux and Michael James Straughan (2004-2006)

Setup: R U R' U R U2 R'

Hyperorientations

U orientation then LR or FB orientation

Robert Smith (2007)

Setup: R U R' U R U2 R'

Permutation > Orientation

Permute First

Corner order then U orientation

Lars Petrus (1981) and various CF methods for two step, one step proposer unknown

Setup: U2 R U2 R' U' R U' R'

Combined

Straughan (object, minimum stickers)

Locate four specific stickers

Michael James Straughan (2024)

Setup: U R U2 R' U' R U R' U2 R' F R F'

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