#2061 ⟨a, b | aab=b, abaa=b⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 9
- Infinite non-cancellative non-commutative monoid
- Element a has infinite order
- Not left cancellative, because left multiplication by b is not injective:
-
b ⋅ a4 = b and b ⋅ 1 = b, however a4 ≠ 1
- Reduction order:
- Left-to-right recursive path with deg(a) = 0; deg(b) = 1
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aab=b,abaa=b a/b - -
baaaa=b
ab=baa
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
6 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 12247 | ⟨a, b | aaab=ab, abaa=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 12381 | ⟨a, b | aaba=ba, abaa=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 18969 | ⟨a, b | aab=b, aaabaa=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 19521 | ⟨a, b | aab=b, aabaa=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 20060 | ⟨a, b | aab=b, aaab=baa⟩ | φ(a) = a, φ(b) = b |
| 11 | 20081 | ⟨a, b | aab=b, abaa=aab⟩ | φ(a) = a, φ(b) = b |