F2L reductions

A worked example

Take this algorithm for the case below. Watching only the two pieces you're solving, partway through it becomes a simpler case:

The first three moves - R' U R - leave the pair in this easier case, which you finish with a basic R U R':

So the database lists this as a reduction: do R' U R, then it's the easier case - no need to memorise the whole string as one block.

The “Show reductions” toggle

Every row spells its whole algorithm, always. What the toggle changes is whether the table marks the points that algorithm passes through an easier case:

• On (default): hover a row (or tap it, on a phone) and the easier case's picture and name appear above the moves, at the point they reach it. An algorithm that steps through more than one easier case gets a marker for each, so you can read the whole chain.
• Off: the rows read as plain move sequences, with nothing marking the reduction points.

The markers float above the row rather than sitting in it, so nothing on screen moves as you run the pointer down the table - and the moves stay exactly the sequence the cube plays while you scrub them.

Reductions are great for learning: if you already know the easier case, you only have to remember the short setup in front of it. The “Fold same reductions” option then groups the algorithms that share a setup into the same easier case onto one row - they only differ in how they finish that case.

Rotation reductions

Sometimes the “setup” is nothing but a cube rotation: turn the whole cube (y, y', d or d') and you're suddenly looking at a case you already know - just in a different slot. No pieces move at all; it's the same position viewed from another angle.

Which of those rotations you pick only changes your grip, not the solve, so they're interchangeable. That's what the “Fold rotations” option (on by default) does: every algorithm that reaches the same easier case by a pure rotation is grouped into a single row with a generic rotation chip, with their usage and votes summed. Turn it off to see each specific rotation as its own row.

The Roux second block, too

The second-block database has the same toggle, and it means the same thing there: most of its cases are these F2L cases (the block is the first two layers' right-hand slots with the front and back bottom edges missing), so a second-block algorithm can just as well pass through an easier one on its way in. It has no rotation reductions, though: Roux keeps the cube in one orientation for the whole solve, so a second-block algorithm has no rotation to fold.