SemiBase

A certified basis of 10 identities

This list of identities is a basis, proved in Lean, of 2 semigroups of order six, all of which generate the variety V[2675]. Removing the identities that follow from the others leaves 3 identities (Vampire); the variety page shows the shortest known basis.

Identifier sb-67d064deade04760 in the data of the bases-min seal.

Certified for

The identities

  1. xyx ≈ yxy
  2. x³y ≈ x²y
  3. x²yx ≈ yxy
  4. x²y³ ≈ xyx
  5. xyzx ≈ yzxy
  6. xyzx ≈ zyxz
  7. x²yzy ≈ xyzx
  8. x²yz² ≈ xyxz²
  9. xy²zt ≈ xyzt
  10. x²yzt ≈ xyxzt