A certified basis of 25 identities
This list of identities is a basis, proved in Lean, of 5 semigroups of order six, all of which generate the variety V[4040]. Removing the identities that follow from the others leaves 3 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-e2a549a27d377069 in the data of the bases-min seal.
Certified for
The identities
- x² ≈ x⁴
- x³yx ≈ xyx
- x³y² ≈ yxy
- x²yx ≈ xyx²
- x²yx ≈ yxy²
- x²yx² ≈ xyx
- x²yxy ≈ yxy
- x²y² ≈ xyxy
- x²y² ≈ xy²x
- x²y² ≈ yx²y
- x²y²x ≈ yxy
- x²y³ ≈ xyx
- xyx ≈ xyx³
- xyx ≈ xyxy²
- xyx ≈ xy²xy
- xyx ≈ xy³x
- xyx ≈ yx²y²
- xyx ≈ yxyxy
- xyx ≈ yxy²x
- xyzx ≈ xzyx
- x²yzy ≈ xzxy²
- xyxzx ≈ zyxz²
- xyxz² ≈ xyzxz
- xyxz² ≈ xyz²x
- xyxz² ≈ zyx²z