SemiBase

A certified basis of 11 identities

This list of identities is a basis, proved in Lean, of 2 semigroups of order six, all of which generate the variety V[880]. Removing the identities that follow from the others leaves 3 identities (Vampire); the variety page shows the shortest known basis.

Identifier sb-ead39309254499e5 in the data of the bases-min seal.

Certified for

The identities

  1. xy ≈ yx
  2. x³ ≈ y³
  3. x²y ≈ xyx
  4. x²y ≈ yx²
  5. xyx ≈ yx²
  6. xyz ≈ xzy
  7. xyz ≈ yxz
  8. xyz ≈ yzx
  9. xyz ≈ zyx
  10. x³ ≈ yztu
  11. xyzt ≈ uvws