#402 ⟨a, b | ababaab=b⟩
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- Properties
- Rewriting system
- Isomorphic instances
- Presentation has sum-of-sides 8
- Infinite non-cancellative non-commutative monoid
- Not right cancellative, because right multiplication by b is not injective:
-
(ab)2a2 ⋅ b = b and 1 ⋅ b = b, however (ab)2a2 ≠ 1
- Enveloping group: ⟨a, b | aabb⟩
- Auxiliary generators:
- c = ab
- Reduction order:
- Left-to-right recursive path with deg(c) = deg(a) = 0, c < a; deg(b) = 1
- Certificate: derivations of all rewriting rules from the defining relations.
- Morphocompletion: how the auxiliary generators were found.
# ab:ababaab=b ca/b ab=c morph:2/0
accc=ccac
accac=c
b=ccac
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 1764 | ⟨a, b | abaabaaab=b⟩ | φ(a) = a, φ(b) = ccc |