#3009 ⟨a, b | aa=a, aaba=ba⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 9
- 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
- Auxiliary generators:
- c = ba
- Reduction order:
- Left-to-right shortlex with a < c < b
- Certificate: derivations of all rewriting rules from the defining relations.
- Morphocompletion: how the auxiliary generators were found.
# ab:aa=a,aaba=ba acb ba=c morph:2/1
aa=a
ac=c
ca=c
ba=c
bc=cc
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
5 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 8849 | ⟨a, b | aa=a, aaaba=ba⟩ | φ(a) = a, φ(b) = b |
| 10 | 9130 | ⟨a, b | aa=a, aaba=baa⟩ | φ(a) = a, φ(b) = b |
| 11 | 24597 | ⟨a, b | aa=a, aaaaba=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 24605 | ⟨a, b | aa=a, aaabaa=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25134 | ⟨a, b | aa=a, aaaba=baa⟩ | φ(a) = a, φ(b) = b |