#896 ⟨a, b | aa=a, babb=a⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 8
- Infinite non-cancellative non-commutative monoid
- Element b has infinite order
- Not left cancellative, because left multiplication by a is not injective:
-
a ⋅ a = a and a ⋅ 1 = a, however a ≠ 1
- Not right cancellative, because right multiplication by a is not injective:
-
a ⋅ a = a and 1 ⋅ a = a, however a ≠ 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:aa=a,babb=a b/a - -
abbbbbb=a
ba=abbbb
aa=a
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
13 total
| Σ | # | Presentation | Mapping |
|---|
| 9 | 2886 | ⟨a, b | aa=a, baabb=a⟩ | φ(a) = a, φ(b) = b |
| 9 | 3029 | ⟨a, b | aa=a, babb=aa⟩ | φ(a) = a, φ(b) = b |
| 10 | 5148 | ⟨a, b | aab=ab, babb=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 8622 | ⟨a, b | aa=a, baaabb=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 8895 | ⟨a, b | aa=a, baabb=aa⟩ | φ(a) = a, φ(b) = b |
| 10 | 9170 | ⟨a, b | aa=a, babb=aaa⟩ | φ(a) = a, φ(b) = b |
| 11 | 12303 | ⟨a, b | aaab=bb, abaa=b⟩ | φ(a) = b, φ(b) = a |
| 11 | 15431 | ⟨a, b | aaa=aa, baabb=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 15647 | ⟨a, b | aab=ab, baabb=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24150 | ⟨a, b | aa=a, baaaabb=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24691 | ⟨a, b | aa=a, baaabb=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 25226 | ⟨a, b | aa=a, baabb=aaa⟩ | φ(a) = a, φ(b) = b |
| 11 | 25700 | ⟨a, b | aa=a, babb=aaaa⟩ | φ(a) = a, φ(b) = b |