#7808 ⟨a, b | aaa=1, baabb=ab⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 10
- Infinite non-cancellative non-commutative monoid
- Element ab has infinite order
- Not left cancellative, because left multiplication by b is not injective:
-
b ⋅ (a2b)2 = b and b ⋅ 1 = b, however (a2b)2 ≠ 1
- Not right cancellative, because right multiplication by b is not injective:
-
ba2b ⋅ b = ab and a ⋅ b = ab, however ba2b ≠ a
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aaa=1,baabb=ab ab - -
aaa=1
baabb=ab
baabab=aab
baabaab=b
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
2 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 21685 | ⟨a, b | aaa=1, aabaabb=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 21715 | ⟨a, b | aaa=1, abaabab=b⟩ | φ(a) = a, φ(b) = b |