#1036 ⟨a, b, c | ab=c, bac=c⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 7
- Infinite non-cancellative non-commutative monoid
- Element a has infinite order
- Not right cancellative, because right multiplication by d is not injective:
-
bd ⋅ d = d and 1 ⋅ d = d, however bd ≠ 1
- Auxiliary generators:
- d = ac
- Reduction order:
- Left-to-right recursive path with deg(b) = deg(d) = 0, b < d; deg(c) = deg(a) = 1, c < a
- Certificate: derivations of all rewriting rules from the defining relations.
- Morphocompletion: how the auxiliary generators were found.
# abc:ab=c,bac=c bd/ca ac=d morph:2/1
bdd=d
c=bd
ab=bd
ad=dd
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 8 | 6066 | ⟨a, b, c | ab=c, bac=ab⟩ | φ(a) = a, φ(b) = b, φ(c) = bd |