#5375 ⟨a, b | aab=ab, aba=ba⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 10
- Infinite non-cancellative non-commutative monoid
- Element a has infinite order
- Not left cancellative, because left multiplication by a is not injective:
-
a ⋅ ab = ab and a ⋅ b = ab, however ab ≠ b
- Not right cancellative, because right multiplication by c is not injective:
-
a ⋅ c = c and 1 ⋅ c = c, 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:aab=ab,aba=ba acb ba=c morph:2/1
ac=c
ba=c
bc=cc
aab=ab
cab=cb
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 16155 | ⟨a, b | aab=ab, aaba=ba⟩ | φ(a) = a, φ(b) = b |