#1693 ⟨a, b | aabababaa=a⟩
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- Properties
- Rewriting system
- Isomorphic instances
- Presentation has sum-of-sides 10
- Infinite non-cancellative non-commutative monoid
- Not left cancellative, because left multiplication by a is not injective:
-
a ⋅ (ab)3a2 = a and a ⋅ 1 = a, however (ab)3a2 ≠ 1
- Not right cancellative, because right multiplication by a is not injective:
-
a2(ba)3 ⋅ a = a and 1 ⋅ a = a, however a2(ba)3 ≠ 1
- Enveloping group: ⟨a, b | aaabb⟩
- Auxiliary generators:
- c = ababa
- Reduction order:
- Left-to-right recursive path with deg(c) = 0; deg(b) = deg(a) = 1, b < a
- Certificate: derivations of all rewriting rules from the defining relations.
- Morphocompletion: how the auxiliary generators were found.
# ab:aabababaa=a c/ba ababa=c morph:5/0
ccbc=cbcc
ccba=cbca
abc=cba
acbc=cbac
caa=aac
cacac=a
cbaac=c
aba=cac
acba=cbaa
cbaaa=a
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 1757 | ⟨a, b | abaaababa=a⟩ | φ(a) = a, φ(b) = b |