SemiBase

A certified basis of 8 identities

This list of identities is a basis, proved in Lean, of 4 semigroups of order six, all of which generate the variety V[7689]. Removing the identities that follow from the others leaves 4 identities (Vampire); the variety page shows the shortest known basis.

Identifier sb-4d3779b5182670a2 in the data of the bases-min seal.

Certified for

The identities

  1. x² ≈ x³
  2. x²yx ≈ xyx
  3. xyx ≈ xyx²
  4. x²y² ≈ xyxy
  5. x²y² ≈ yx²y
  6. x²yz ≈ xyxz
  7. xyxzx ≈ xyzx
  8. x²yzy ≈ yx²zy