#967 ⟨a, b | aa=a, bab=ab⟩
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 ⋅ a = a and a ⋅ 1 = a, however a ≠ 1
- Not right cancellative, because right multiplication by a is not injective:
-
a ⋅ a = a and 1 ⋅ a = a, however a ≠ 1
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aa=a,bab=ab ab - -
aa=a
bab=ab
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
9 total
| Σ | # | Presentation | Mapping |
|---|
| 9 | 3027 | ⟨a, b | aa=a, baab=ab⟩ | φ(a) = a, φ(b) = b |
| 9 | 3145 | ⟨a, b | aa=a, bab=aab⟩ | φ(a) = a, φ(b) = b |
| 10 | 8893 | ⟨a, b | aa=a, baaab=ab⟩ | φ(a) = a, φ(b) = b |
| 10 | 9123 | ⟨a, b | aa=a, aaab=bab⟩ | φ(a) = a, φ(b) = b |
| 10 | 9165 | ⟨a, b | aa=a, baab=aab⟩ | φ(a) = a, φ(b) = b |
| 11 | 24689 | ⟨a, b | aa=a, baaaab=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25127 | ⟨a, b | aa=a, aaaab=bab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25221 | ⟨a, b | aa=a, baaab=aab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25691 | ⟨a, b | aa=a, baab=aaab⟩ | φ(a) = a, φ(b) = b |