#508 ⟨a, b, c | ab=aa, bc=a⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 7
- Infinite non-cancellative non-commutative monoid
- Element a has infinite order
- Not left cancellative, because left multiplication by a is not injective:
-
a ⋅ b = a2 and a ⋅ a = a2, however b ≠ a
- Reduction order:
- Left-to-right shortlex with a < b < c
- Certificate: derivations of all rewriting rules from the defining relations.
# abc:ab=aa,bc=a abc - -
ab=aa
bc=a
aac=aa
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
2 total
| Σ | # | Presentation | Mapping |
|---|
| 8 | 6022 | ⟨a, b, c | ab=c, aba=cc⟩ | φ(a) = b, φ(b) = c, φ(c) = a |
| 8 | 6029 | ⟨a, b, c | ab=c, abc=ca⟩ | φ(a) = b, φ(b) = c, φ(c) = a |