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[7974]. Removing the identities that follow from the others leaves 5 identities (Vampire); the variety page shows the shortest known basis.

Identifier sb-79ed57d454074b42 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. xyzx ≈ xzyx
  7. x²y²z ≈ xy²xz
  8. x²yzty ≈ xzxyty
  9. x²yzty ≈ xzxyty