A certified basis of 16 identities
This list of identities is a basis, proved in Lean, of 9 semigroups of order six, all of which generate the variety V[4089]. Removing the identities that follow from the others leaves 5 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-b2b0311735eaab62 in the data of the bases-min seal.
Certified for
The identities
- x² ≈ x⁴
- x³yx ≈ xyx
- x²yx ≈ xyx²
- x²yx² ≈ xyx
- x²y² ≈ xyxy
- x²y² ≈ xy²x
- x²y² ≈ yx²y
- xyx ≈ xyx³
- x³y² ≈ yx³y
- x²yzx ≈ xyxzx
- x²yzy ≈ xyxzy
- x²yzy ≈ yx²zy
- xyxz² ≈ xyzxz
- xyxz² ≈ xyz²x
- xyzxy ≈ xyzyx
- xyzxy ≈ yxzxy