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[9699]. Removing the identities that follow from the others leaves 2 identities (Vampire); the variety page shows the shortest known basis.

Identifier sb-fdc2f36333029785 in the data of the bases-min seal.

Certified for

The identities

  1. x³ ≈ x⁴
  2. xyx ≈ xy²
  3. x³y ≈ x²y
  4. x²y ≈ x²yx
  5. x²y ≈ x²y²
  6. xyx ≈ xyx²
  7. xyxz ≈ xyz
  8. x²yz ≈ x²zy