#642 ⟨a, b | ab=aa, bba=a⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 8
- Infinite non-cancellative non-commutative monoid
- Element b has infinite order
- Not left cancellative, because left multiplication by a is not injective:
-
a ⋅ b = a2 and a ⋅ a = a2, however b ≠ a
- Not right cancellative, because right multiplication by a is not injective:
-
b2 ⋅ a = a and 1 ⋅ a = a, however b2 ≠ 1
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:ab=aa,bba=a ab - -
ab=aa
bba=a
aaaa=aa
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
4 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 4196 | ⟨a, b | bab=baa, bba=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 6673 | ⟨a, b | aab=b, aaba=bb⟩ | φ(a) = b, φ(b) = a |
| 10 | 6676 | ⟨a, b | aab=b, aabb=ba⟩ | φ(a) = b, φ(b) = a |
| 10 | 6700 | ⟨a, b | aab=b, baab=ba⟩ | φ(a) = b, φ(b) = a |