SemiBase

A certified basis of 9 identities

This list of identities is a basis, proved in Lean, of 6 semigroups of order six, all of which generate the variety V[7954]. Removing the identities that follow from the others leaves 4 identities (Vampire); the variety page shows the shortest known basis.

Identifier sb-cda56e6cd3180e3e in the data of the bases-min seal.

Certified for

The identities

  1. x² ≈ x³
  2. x²yx ≈ xyx
  3. xyx ≈ xyx²
  4. xyxy ≈ xy²x
  5. xyxzx ≈ xyzx
  6. xyxzy ≈ xy²zx
  7. xyxzy ≈ xyzxy
  8. xyxzy ≈ xyzyx
  9. xyzxz ≈ xyz²x