SemiBase

A certified basis of 9 identities

This list of identities is a basis, proved in Lean, of 3 semigroups of order six, all of which generate the variety V[881]. Removing the identities that follow from the others leaves 2 identities (Vampire); the variety page shows the shortest known basis.

Identifier sb-a421756b24262c3f in the data of the bases-min seal.

Certified for

The identities

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