#1672 ⟨a, b | aba=ab, bba=a⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 9
- Infinite non-cancellative non-commutative monoid
- Element b has infinite order
- Not left cancellative, because left multiplication by a is not injective:
-
a ⋅ ba = ab and a ⋅ b = ab, however ba ≠ b
- Not right cancellative, because right multiplication by a is not injective:
-
b2 ⋅ a = a and 1 ⋅ a = a, however b2 ≠ 1
- Reduction order:
- Left-to-right recursive path with deg(b) = 0; deg(a) = 1
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aba=ab,bba=a b/a - -
abbb=ab
bba=a
aa=abb
aba=ab
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
4 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 19526 | ⟨a, b | aab=b, aabab=ba⟩ | φ(a) = b, φ(b) = a |
| 11 | 19574 | ⟨a, b | aab=b, baaab=ba⟩ | φ(a) = b, φ(b) = a |
| 11 | 20069 | ⟨a, b | aab=b, aaba=bab⟩ | φ(a) = b, φ(b) = a |
| 11 | 20090 | ⟨a, b | aab=b, abab=aba⟩ | φ(a) = b, φ(b) = a |