SemiBase

A certified basis of 7 identities

This list of identities is a basis, proved in Lean, of 2 semigroups of order six, all of which generate the variety V[7980]. Removing the identities that follow from the others leaves 5 identities (Vampire); the variety page shows the shortest known basis.

Identifier sb-2b84b5b45aabb16b in the data of the bases-min seal.

Certified for

The identities

  1. x² ≈ x³
  2. x²yx ≈ xyx
  3. xyx ≈ xyx²
  4. xyxy ≈ yx²y
  5. xyzx ≈ xzyx
  6. xyxyz ≈ xy²xz
  7. xyxzy ≈ yx²zy