#26689 ⟨a, b | aa=1, babbbbab=b⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 11
- Infinite non-cancellative non-commutative monoid
- Element ac has infinite order
- Not left cancellative, because left multiplication by b is not injective:
-
b ⋅ bac = bacb and b ⋅ acb = bacb, however bac ≠ acb
- Not right cancellative, because right multiplication by c is not injective:
-
bca ⋅ c = bac2 and bac ⋅ c = bac2, however bca ≠ bac
- Auxiliary generators:
- c = bab
- Reduction order:
- Left-to-right shortlex with a < b < c
- Certificate: derivations of all rewriting rules from the defining relations.
- Morphocompletion: how the auxiliary generators were found.
# ab:aa=1,babbbbab=b abc bab=c morph:3/0
aa=1
bab=c
cab=bac
bbac=bacb
bcac=bacc
cbac=cacb
cbbb=bbbc
cbbc=b
ccac=cacc
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 26701 | ⟨a, b | aa=1, bbababbb=b⟩ | φ(a) = a, φ(b) = b |