YruRU

YruRU (pronounced WhyRooRoo) is a 3x3x3 method designed specifically for OneHanded Solving. It is a CPfirst method that relies on reduced movesets to ensure great ergonomics for OH turning. The name YruRU is said to stand for Yash's ruRU reduction, but can also be interpreted as "Why Roux?", a dig on Roux, which is widely regarded as the optimal OH speedsolving method known. While it is considered by some critics to be similar to other CPfirst methods such as Briggs or 2GR now deemed infeasible for speedsolving, YruRU has a significantly different approach to Corner Permutation, first block and edge orientation.
Overview
 CPline: First, a 1x1x3 block is solved in the bottomleft of the cube (for lefthanded OH solvers), while simultaneously solving corner permutation. We get a CPskip once every 6 solves. This step takes 46 moves on average, and following this step the entire cube is solved using <r, u, R, U>.
 pEOextension: In this step, the 1x1x3 line is extended to form a 1x2x3 block, while simultaneously orienting 23 of the remaining edges and ensuring one of the oriented edges ends up in DB. This is done to ensure that the following step can be executed with minimal pause for recognition. While completely intuitive, it can be broken into 18 cases after achieving a "setup configuration" and solved using 5move algorithms. Since CPline takes very few moves, it is usually possible to inspect up to and influence the setup configuration. This step takes 79 moves on average, and following this step, the entire cube is solved using <r, R, U>.
 EOBF: A step reminiscent of LEOR type methods, this step attempts to achieve a solved edge orientation, followed by solving of the DB and DF edges. However, due to the partial edge orientation already done, the casecount is severely restricted, and the orienting of the DB edge allows for very quick recognition of the EO case. Thus, the biggest drawback of LEORtype is addressed effectively. While completely intuitive, the EO can be broken into ~40 cases with 57 move algorithms. The final two moves of the algorithm are flexible, which allows for easy influence of BF. This step takes 911 moves on average, and following this step, the entire cube is solved using <R, U>.
 F2L: This is identical to solving a block in ZZ, however there is a choice of two bottom colours. This step takes ~15 moves in a speedsolve, although given extremely simple lookahead and the most ergonomic OH moveset possible, it is easy to execute it at very high TPS.
 LL: There are 84 possible cases for LL called 2GLLs. The recognition of these cases is substantially easier than ZBLL recognition due to the knowledge of solved CP; in fact it is arguably simpler than PLL recognition. The algorithms are on average 13 moves long, and are 2gen, leading to very high TPS.
Algorithms
2GLL algorithms are widely available online.
The idea to do EO is, as soon as the FB+pEO is done, intuit the number of bad edges present on the cube. Since all bad edges will be in the field of view, the accuracy of doing this will be near perfect given the small discrete set {0 (2%), 2 (36%), 4 (53%), 6 (9%)}. Then, identify the case and do the algorithm. The recognition speed should be comparable to OLL. Here is an exhaustive list of cases to be memorised, however all these are completely intuitive.
Note, the last two moves can be any one of U r, U' r, U r', U' r'
2 bad edges:
DF is bad: set up the other edge to one of these positions:
 UR: r U' R' U r
 RD: r U' R U r
 RB: r U' R2 U r
DF is good, both bad edges in U layer:
 UFUB: r U' r U' R' U r
 UFUR: r U R' U r (mirror for UBUR)
DF is good, one bad edge in U layer:
 UFRD: r U R U r (mirror for UBRD)
 UFRB: r U R2 U r (mirror for UBRF)
 UFRF: R' r U R U r (mirror for UBRB)
If DF is good and both bad edges are in R layer: bring one of them to UF/UB:
 RBRD: R' U r U R2 U r (mirror for RDRF)
 RFRB: R U r U R U r
All other cases' optimal solutions are 1 move setups to these (i.e. using R/U moves).
4 bad edges:
DF is bad: all (except one special case) optimal solutions are 03 move setups to staircase (ULUFRF) [or to arrow (ULUFUR) which basically sets up to staircase]:
 Staircase: r U r
 Arrow: R' r U r
 UFULRD: R r U r
 UFULRB: R2 r U r
 UFUBRF: R U R' r U r
 UFUBRD: R2 U R' r U r
 UFUBRB: R' U R' r U r
 UFRFRD: R U r U r
 UFRBRD: R2 U r U r
 RFRBRD: R U R U r U r
 Special case  UFRFRB: r U2 R2 U r
DF is good: make DF/DB bad using r U2 r or r2, then convert to staircase (or arrow)
 UFURUBUL: r U2 r' U2 r U r
 UFUBRFRB: r U2 r U' r U r
 UFUBRBRD: r U2 r U2 r U r (mirror for UFUBRFRD)
 UFURRFRD: r2 U' R' U' r' U r (mirror for UBURRBRD)
 UFULRFRB: r2 U r U2 r2 U r
 UFRFRDRB: r2 U' r U2 r2 U r
 UFURUBRF: r U' r' U2 r U r (mirror for UFURUBRB)
 UFURUBRD: R r U2 r U' r U r
All other cases' optimal (or 1 move over optimal) solutions are 1 move setups to these (i.e. using RU moves)
6 bad edges:
Here, I will denote the case using good edges instead of bad edges: If DF is bad, simply put the two good edges in UR and DR using <R, U> moves, and do r' U' r2 U r
DF is bad, Both good edges in U layer:
 UFUR: R2 U' r' U' r2 U r
 ULUR: R2 U2 r' U' r2 U r
DF is bad, One good edge in U layer:
 UFRF: R' U' r' U' r2 U r (mirror for UBRB)
 UFRD: U' r' U' r2 U r
DF is bad, Both good edges in R layer:
 RFRB: R r' U' r2 U r
 RFRD: R U R' U' r' U' r2 U r (mirror for RBRD)
DF is good: Put the only other good edge in UR:
 UR: r U2 r U' r' U' r2 U r
Pros
 Move set gets progressively ergonomic over the solve.
 Fairly low movecount compared to CFOP with similar number of algorithms.
 Extremely high TPS possible, especially for the latter parts of the solve.
Cons
 CPline is a difficult concept to master.
 The EO step usually requires a pause for recognition for most solvers.
 u moves are not very ergonomic for OneHanded solving.
Walkthrough Solves
Scramble: D' B' R' D R2 U' D' F R D2 L' B2 L2 D2 R F2 U2 F2 U2 L F'
y' // Inspection
F' U' F U2 S' // CPLine
r2 E R U' // Setup
u' R u' U r // FB+pEO
R r U2 r U' r U' r // EO
R U r2 // BF
U R2 U2 R2 // Square
U2 R' U' R U R' // F2L
U2 R' U2 R2 U2 R2 U' R2 U' R2 U R // 2GLL
Scramble: D' L F' U' R' L D R D2 F2 R2 D2 F2 L' U2 D2 L' B D2
x' // Inspection
r' U' f' U' F // CPline
r U u R' u2 R' U // Setup
u R' u U r // FB+pEO
R U' r' U' r2 U' r // EO
U r2 // BF
U R U' R' U R2 // Square
U2 R' U2 R U2 R' U R U2 R' // F2L + cancelled moves
U2 R' U' R U' R' U2 R U' // 2GLL