#2063 ⟨a, b | aab=b, abab=b⟩
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 b is not injective:
-
b ⋅ b = b and b ⋅ 1 = b, however b ≠ 1
- Not right cancellative, because right multiplication by b is not injective:
-
b ⋅ b = b and 1 ⋅ b = b, however b ≠ 1
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aab=b,abab=b ab - -
bb=b
aab=b
bab=ab
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
8 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 12249 | ⟨a, b | aaab=ab, abab=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 12383 | ⟨a, b | aaba=ba, abab=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 18971 | ⟨a, b | aab=b, aaabab=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 18995 | ⟨a, b | aab=b, abaaab=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 19525 | ⟨a, b | aab=b, aabab=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 19573 | ⟨a, b | aab=b, baaab=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 20061 | ⟨a, b | aab=b, aaab=bab⟩ | φ(a) = a, φ(b) = b |
| 11 | 20089 | ⟨a, b | aab=b, abab=aab⟩ | φ(a) = a, φ(b) = b |