#12289 ⟨a, b | aaab=ba, babb=b⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 11
- Infinite non-cancellative non-commutative monoid
- Element a has infinite order
- Not left cancellative, because left multiplication by b is not injective:
-
b ⋅ b4 = b and b ⋅ 1 = b, however b4 ≠ 1
- Not right cancellative, because right multiplication by b is not injective:
-
b4 ⋅ b = b and 1 ⋅ b = b, however b4 ≠ 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:aaab=ba,babb=b b/a - -
bbbbb=b
ba=bbb
aaab=bbb
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
2 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 12293 | ⟨a, b | aaab=ba, bbab=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 12295 | ⟨a, b | aaab=ba, bbba=b⟩ | φ(a) = a, φ(b) = b |