#21777 ⟨a, b | aaa=1, babbbab=b⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 11
- Infinite non-cancellative non-commutative monoid
- Element ba2 has infinite order
- Not left cancellative, because left multiplication by b is not injective:
-
b ⋅ abc = bcab and b ⋅ cab = bcab, however abc ≠ cab
- Not right cancellative, because right multiplication by c is not injective:
-
bac ⋅ c = bcac and bca ⋅ c = bcac, however bac ≠ bca
- Auxiliary generators:
- c = bb
- Reduction order:
- Left-to-right shortlex with b < c < a
- Certificate: derivations of all rewriting rules from the defining relations.
- Morphocompletion: how the auxiliary generators were found.
# ab:aaa=1,babbbab=b bca bb=c morph:2/0
bb=c
cb=bc
aaa=1
babc=bcab
bacc=bcac
cabc=ccab
cacc=ccac
cabab=babac
cabac=b
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 21785 | ⟨a, b | aaa=1, bbababb=b⟩ | φ(a) = a, φ(b) = b |