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[9677]. Removing the identities that follow from the others leaves 2 identities (Vampire); the variety page shows the shortest known basis.

Identifier sb-72341c1c1593b4a5 in the data of the bases-min seal.

Certified for

The identities

  1. x³ ≈ x⁴
  2. x²y ≈ xy²
  3. x³y ≈ x²y
  4. x²y ≈ xyxy
  5. x²yx ≈ xyx
  6. x²yz ≈ xyz
  7. xyxz ≈ xyz
  8. xyz ≈ xzyz