#1133 ⟨a, b | aa=1, bbabb=b⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 8
- Infinite non-cancellative non-commutative monoid
- Element ba has infinite order
- Not left cancellative, because left multiplication by b is not injective:
-
b ⋅ ab3 = b and b ⋅ 1 = b, however ab3 ≠ 1
- Not right cancellative, because right multiplication by b is not injective:
-
bab2 ⋅ b = b and 1 ⋅ b = b, however bab2 ≠ 1
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aa=1,bbabb=b ab - -
aa=1
bbab=babb
babbb=b
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
5 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 9707 | ⟨a, b | aa=1, aabbabb=b⟩ | φ(a) = a, φ(b) = b |
| 10 | 9771 | ⟨a, b | aa=1, baababb=b⟩ | φ(a) = a, φ(b) = b |
| 10 | 9789 | ⟨a, b | aa=1, bbaaabb=b⟩ | φ(a) = a, φ(b) = b |
| 10 | 10014 | ⟨a, b | aa=1, abbabb=ab⟩ | φ(a) = a, φ(b) = b |
| 10 | 10333 | ⟨a, b | aa=1, bbabb=aab⟩ | φ(a) = a, φ(b) = b |