#5152 ⟨a, b | aab=ab, bbab=a⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 10
- 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:
- Right-to-left recursive path with deg(b) = 0; deg(a) = 1
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aab=ab,bbab=a reversed:b/a - -
bbbbbba=a
ab=bbbba
aa=a
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
10 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 5268 | ⟨a, b | aba=ab, bbab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 14612 | ⟨a, b | aaba=b, aabab=b⟩ | φ(a) = b, φ(b) = a |
| 11 | 14614 | ⟨a, b | aaba=b, aabba=b⟩ | φ(a) = b, φ(b) = a |
| 11 | 14636 | ⟨a, b | aaba=b, baaab=b⟩ | φ(a) = b, φ(b) = a |
| 11 | 14638 | ⟨a, b | aaba=b, baaba=b⟩ | φ(a) = b, φ(b) = a |
| 11 | 14642 | ⟨a, b | aaba=b, babaa=b⟩ | φ(a) = b, φ(b) = a |
| 11 | 14650 | ⟨a, b | aaba=b, bbaaa=b⟩ | φ(a) = b, φ(b) = a |
| 11 | 15659 | ⟨a, b | aab=ab, bbaab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 15891 | ⟨a, b | aba=ab, bbaab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 15893 | ⟨a, b | aba=ab, bbaba=a⟩ | φ(a) = a, φ(b) = b |