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[12198]. Removing the identities that follow from the others leaves 3 identities (Vampire); the variety page shows the shortest known basis.

Identifier sb-dd41982bbb107f6b in the data of the bases-min seal.

Certified for

The identities

  1. x²y ≈ xy
  2. xy ≈ xy²
  3. xyx ≈ xy²x
  4. xyxy ≈ xy²
  5. xyzx ≈ xyzyx
  6. xyzx ≈ xyz²x
  7. xyzxy ≈ xyzy
  8. xyzxz ≈ xyz²
  9. xyztx ≈ xyztzx
  10. xyztxz ≈ xyztz