#1243 ⟨a, b, c | aa=1, abcb=b⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 7
- Infinite non-cancellative non-commutative monoid
- Element ba has infinite order
- Not left cancellative, because left multiplication by b is not injective:
-
b ⋅ cab = b and b ⋅ 1 = b, however cab ≠ 1
- Not right cancellative, because right multiplication by b is not injective:
-
bca ⋅ b = b and 1 ⋅ b = b, however bca ≠ 1
- Reduction order:
- Left-to-right shortlex with a < b < c
- Certificate: derivations of all rewriting rules from the defining relations.
# abc:aa=1,abcb=b abc - -
aa=1
bcb=ab
bcab=b
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 7 | 1430 | ⟨a, b, c | aa=1, bcb=ab⟩ | φ(a) = a, φ(b) = b, φ(c) = c |