#3120 ⟨a, b | ab=a, bbaa=aa⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 9
- Infinite non-cancellative non-commutative monoid
- Element a has infinite order
- Not left cancellative, because left multiplication by a is not injective:
-
a ⋅ b = a and a ⋅ 1 = a, however b ≠ 1
- Not right cancellative, because right multiplication by a is not injective:
-
b2a ⋅ a = a2 and a ⋅ a = a2, however b2a ≠ a
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:ab=a,bbaa=aa ab - -
ab=a
bbaa=aa
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
14 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 9084 | ⟨a, b | ab=a, bbaab=aa⟩ | φ(a) = a, φ(b) = b |
| 10 | 9088 | ⟨a, b | ab=a, bbaba=aa⟩ | φ(a) = a, φ(b) = b |
| 10 | 9353 | ⟨a, b | ab=a, bbaa=aab⟩ | φ(a) = a, φ(b) = b |
| 10 | 9354 | ⟨a, b | ab=a, bbaa=aba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25064 | ⟨a, b | ab=a, bbaabb=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 25072 | ⟨a, b | ab=a, bbabab=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 25076 | ⟨a, b | ab=a, bbabba=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 25605 | ⟨a, b | ab=a, bbaab=aab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25606 | ⟨a, b | ab=a, bbaab=aba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25613 | ⟨a, b | ab=a, bbaba=aab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25614 | ⟨a, b | ab=a, bbaba=aba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25861 | ⟨a, b | ab=a, bbaa=aabb⟩ | φ(a) = a, φ(b) = b |
| 11 | 25863 | ⟨a, b | ab=a, bbaa=abab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25864 | ⟨a, b | ab=a, bbaa=abba⟩ | φ(a) = a, φ(b) = b |