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[2683]. Removing the identities that follow from the others leaves 4 identities (Vampire); the variety page shows the shortest known basis.

Identifier sb-9461703f2f0fd7b8 in the data of the bases-min seal.

Certified for

The identities

  1. x³y ≈ x²y
  2. x²y²x ≈ y²x²y
  3. x²yz ≈ xyxz
  4. xyzx ≈ xzyx
  5. xyzy ≈ xzy²
  6. x²yzy ≈ yzx²y
  7. x²y²z² ≈ zx²y²z
  8. xyzt ≈ xzyt