SemiBase

A certified basis of 8 identities

This list of identities is a basis, proved in Lean, of 2 semigroups of order six, all of which generate the variety V[1349]. Removing the identities that follow from the others leaves 4 identities (Vampire); the variety page shows the shortest known basis.

Identifier sb-daf323a774c688a2 in the data of the bases-min seal.

Certified for

The identities

  1. x² ≈ x⁴
  2. x²y ≈ xyx
  3. x³y ≈ yxy²
  4. x³y² ≈ yxy
  5. x²y² ≈ yx²y
  6. xyx ≈ xy³x
  7. xyz ≈ xyz³
  8. xyzx ≈ xzyx