#1587 ⟨a, b | aaaababaa=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 ⋅ a3baba2 = a and a ⋅ 1 = a, however a3baba2 ≠ 1
- Not right cancellative, because right multiplication by a is not injective:
-
a4(ba)2 ⋅ a = a and 1 ⋅ a = a, however a4(ba)2 ≠ 1
- Enveloping group: ⟨a, b | aaaabb⟩
- Auxiliary generators:
- c = ababa
- Reduction order:
- Left-to-right recursive path with deg(a) = deg(c) = 0, a < c; deg(b) = 1
- Certificate: derivations of all rewriting rules from the defining relations.
- Morphocompletion: how the auxiliary generators were found.
# ab:aaaababaa=a ac/b ababa=c morph:5/0
ca=ac
aaaac=a
aaacc=c
cba=abc
cbc=abaaccc
aaaaaba=abaaaaa
aaaaabc=aba
ababa=c
ababc=aaccc
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
2 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 1623 | ⟨a, b | aaababaaa=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 1749 | ⟨a, b | abaaaaaba=a⟩ | φ(a) = a, φ(b) = b |