#9082 ⟨a, b | ab=a, bbaaa=ba⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 10
- Infinite non-cancellative non-commutative monoid
- Element b has infinite order
- Not left cancellative, because left multiplication by a is not injective:
-
a ⋅ b = a and a ⋅ 1 = a, however b ≠ 1
- Not right cancellative, because right multiplication by a is not injective:
-
b2 ⋅ a = ba and b ⋅ a = ba, however b2 ≠ b
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:ab=a,bbaaa=ba ab - -
ab=a
bba=ba
aaaa=aa
baaa=ba
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
4 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 25058 | ⟨a, b | ab=a, bbaaab=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25062 | ⟨a, b | ab=a, bbaaba=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25070 | ⟨a, b | ab=a, bbabaa=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25601 | ⟨a, b | ab=a, bbaaa=bab⟩ | φ(a) = a, φ(b) = b |