#1996 ⟨a, b | aaa=a, babb=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 ⋅ a2 = a and a ⋅ 1 = a, however a2 ≠ 1
- Not right cancellative, because right multiplication by a is not injective:
-
a2 ⋅ a = a and 1 ⋅ a = a, however a2 ≠ 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:aaa=a,babb=a b/a - -
abbbbbb=a
ba=abbbb
aaa=a
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
4 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 12260 | ⟨a, b | aaab=ab, babb=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 12394 | ⟨a, b | aaba=ba, babb=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 18742 | ⟨a, b | aaa=a, baaabb=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 19834 | ⟨a, b | aaa=a, babb=aaa⟩ | φ(a) = a, φ(b) = b |