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[13562]. Removing the identities that follow from the others leaves 7 identities (Vampire); the variety page shows the shortest known basis.

Identifier sb-e0b71ed64d7c31bc in the data of the bases-min seal.

Certified for

The identities

  1. x² ≈ x³
  2. xyx ≈ xyx²
  3. xyxy ≈ xy²x
  4. x²y² ≈ x²y²x
  5. xyzxy ≈ xyzyx
  6. xyzxz ≈ xyz²x
  7. xyztxz ≈ xyztzx