#1689 ⟨a, b | aababaaba=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(aba)2 = a and a ⋅ 1 = a, however ab(aba)2 ≠ 1
- Not right cancellative, because right multiplication by a is not injective:
-
a(ab)2a2b ⋅ a = a and 1 ⋅ a = a, however a(ab)2a2b ≠ 1
- Enveloping group is isomorphic to ℤ
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aababaaba=a ab
abaa=aaba
aaabababa=a
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 1765 | ⟨a, b | abaabaaba=a⟩ | φ(a) = a, φ(b) = b |