SemiBase

A certified basis of 8 identities

This list of identities is a basis, proved in Lean, of 3 semigroups of order six, all of which generate the variety V[13356]. Removing the identities that follow from the others leaves 6 identities (Vampire); the variety page shows the shortest known basis.

Identifier sb-eafa081e11d5582a in the data of the bases-min seal.

Certified for

The identities

  1. x² ≈ x³
  2. x²yx ≈ xyx
  3. xyx ≈ xyx²
  4. xyxy ≈ xy²x
  5. xyxzx ≈ xyzx
  6. xyzxy ≈ xyzyx
  7. xyzxz ≈ xyz²x
  8. xyzyz ≈ xzy²z