SemiBase

A certified basis of 9 identities

This list of identities is a basis, proved in Lean, of 2 semigroups of order six, all of which generate the variety V[13184]. Removing the identities that follow from the others leaves 3 identities (Vampire); the variety page shows the shortest known basis.

Identifier sb-5b3a8e732d09d3da in the data of the bases-min seal.

Certified for

The identities

  1. x² ≈ x³
  2. xyx ≈ xyx²
  3. xyx ≈ xy²x
  4. xyxy ≈ xy²
  5. xyx ≈ xyxyx
  6. xyxz ≈ xy²z
  7. xyzx ≈ xyzyx
  8. xyzxy ≈ xyzy
  9. xyzxz ≈ xyz²