#5285 ⟨a, b | aba=bb, abba=b⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 10
- Infinite non-cancellative non-commutative monoid
- Element a has infinite order
- Not left cancellative, because left multiplication by b is not injective:
-
b ⋅ b6 = b and b ⋅ 1 = b, however b6 ≠ 1
- Not right cancellative, because right multiplication by b is not injective:
-
b6 ⋅ b = b and 1 ⋅ b = b, however b6 ≠ 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=bb,abba=b b/a - -
bbbbbbb=b
ba=abbbbb
aab=bbbb
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
3 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 12364 | ⟨a, b | aaba=ab, baab=a⟩ | φ(a) = b, φ(b) = a |
| 11 | 14842 | ⟨a, b | abba=b, aabaa=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 15914 | ⟨a, b | aba=bb, aabaa=b⟩ | φ(a) = a, φ(b) = b |