#768 ⟨a, b | aaababaa=a⟩
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- Properties
- Rewriting system
- Isomorphic instances
- Presentation has sum-of-sides 9
- Infinite non-cancellative non-commutative monoid
- Not left cancellative, because left multiplication by a is not injective:
-
a ⋅ a(ab)2a2 = a and a ⋅ 1 = a, however a(ab)2a2 ≠ 1
- Not right cancellative, because right multiplication by a is not injective:
-
a3(ba)2 ⋅ a = a and 1 ⋅ a = a, however a3(ba)2 ≠ 1
- Enveloping group: ⟨a, b | aaabb⟩
- Auxiliary generators:
- c = aba
- Reduction order:
- Left-to-right shortlex with b < a < c
- Certificate: derivations of all rewriting rules from the defining relations.
- Morphocompletion: how the auxiliary generators were found.
# ab:aaababaa=a bac aba=c morph:3/0
aba=c
cba=abc
aabc=abca
acbc=abcc
cabc=cbca
caaa=aaac
caac=a
ccbc=cbcc
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 9 | 833 | ⟨a, b | abaaaaba=a⟩ | φ(a) = a, φ(b) = b |