SemiBase

A certified basis of 11 identities

This list of identities is a basis, proved in Lean, of 2 semigroups of order six, all of which generate the variety V[14907]. Removing the identities that follow from the others leaves 3 identities (Vampire); the variety page shows the shortest known basis.

Identifier sb-36facfa49854bd9e in the data of the bases-min seal.

Certified for

The identities

  1. x² ≈ x⁵
  2. x⁴y ≈ xy
  3. x²yx ≈ xyx²
  4. x²y² ≈ xyxy
  5. x²y² ≈ xy²x
  6. x³yx ≈ xy⁴
  7. x²y³ ≈ xy³x
  8. x²yz ≈ xyxz
  9. xyzx ≈ xzyx
  10. xyzy ≈ xzy²
  11. x²yzy ≈ xy²zx