SemiBase

A certified basis of 8 identities

This list of identities is a basis, proved in Lean, of 5 semigroups of order six, all of which generate the variety V[7397]. Removing the identities that follow from the others leaves 3 identities (Vampire); the variety page shows the shortest known basis.

Identifier sb-78143bd4c961098e in the data of the bases-min seal.

Certified for

The identities

  1. x² ≈ x³
  2. x²yx ≈ xyx
  3. xyx ≈ xyx²
  4. xyx ≈ xyxy
  5. xyx ≈ xy²x
  6. xyzx ≈ xzyx
  7. xyzy ≈ xzyz
  8. xyzx ≈ xyz²x