A certified basis of 26 identities
This list of identities is a basis, proved in Lean, of 3 semigroups of order six, all of which generate the variety V[2852]. Removing the identities that follow from the others leaves 3 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-99bcbc9eac862ef7 in the data of the bases-min seal.
Certified for
The identities
- x³ ≈ x⁵
- x⁴y ≈ x²y
- x³yx ≈ xyx
- x³y² ≈ xy²
- x²yx ≈ xyx²
- x²yx ≈ xy³
- x²yx ≈ yx³
- x²yx² ≈ xyx
- x²yxy ≈ yxy
- x²y²x ≈ yxy
- x²y³ ≈ xyx
- xyx ≈ xyx³
- xyx ≈ xyxy²
- xyx ≈ xy²xy
- xyx ≈ xy³x
- xyx ≈ yx⁴
- xyx ≈ yx²y²
- xyx ≈ yxyxy
- xyx ≈ yxy²x
- xyxy ≈ xy²x
- xyxy ≈ yx²y
- x³yz ≈ xyz
- xyxz ≈ yx²z
- xyzx ≈ xzyx
- xyzx ≈ yxzx
- xyz² ≈ yxz²