#3178 ⟨a, b | ab=a, baa=aaa⟩
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 ⋅ b = a and a ⋅ 1 = a, however b ≠ 1
- Not right cancellative, because right multiplication by a is not injective:
-
ba ⋅ a = a3 and a2 ⋅ a = a3, however ba ≠ a2
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:ab=a,baa=aaa ab - -
ab=a
baa=aaa
aaaa=aaa
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
20 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 9268 | ⟨a, b | ab=a, aaab=baa⟩ | φ(a) = a, φ(b) = b |
| 10 | 9276 | ⟨a, b | ab=a, aaba=baa⟩ | φ(a) = a, φ(b) = b |
| 10 | 9292 | ⟨a, b | ab=a, abaa=baa⟩ | φ(a) = a, φ(b) = b |
| 10 | 9328 | ⟨a, b | ab=a, baab=aaa⟩ | φ(a) = a, φ(b) = b |
| 10 | 9336 | ⟨a, b | ab=a, baba=aaa⟩ | φ(a) = a, φ(b) = b |
| 11 | 25432 | ⟨a, b | ab=a, aaabb=baa⟩ | φ(a) = a, φ(b) = b |
| 11 | 25448 | ⟨a, b | ab=a, aabab=baa⟩ | φ(a) = a, φ(b) = b |
| 11 | 25456 | ⟨a, b | ab=a, aabba=baa⟩ | φ(a) = a, φ(b) = b |
| 11 | 25480 | ⟨a, b | ab=a, abaab=baa⟩ | φ(a) = a, φ(b) = b |
| 11 | 25488 | ⟨a, b | ab=a, ababa=baa⟩ | φ(a) = a, φ(b) = b |
| 11 | 25504 | ⟨a, b | ab=a, abbaa=baa⟩ | φ(a) = a, φ(b) = b |
| 11 | 25556 | ⟨a, b | ab=a, baabb=aaa⟩ | φ(a) = a, φ(b) = b |
| 11 | 25572 | ⟨a, b | ab=a, babab=aaa⟩ | φ(a) = a, φ(b) = b |
| 11 | 25580 | ⟨a, b | ab=a, babba=aaa⟩ | φ(a) = a, φ(b) = b |
| 11 | 25829 | ⟨a, b | ab=a, baab=aaab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25830 | ⟨a, b | ab=a, baab=aaba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25832 | ⟨a, b | ab=a, baab=abaa⟩ | φ(a) = a, φ(b) = b |
| 11 | 25838 | ⟨a, b | ab=a, baba=aaab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25839 | ⟨a, b | ab=a, baba=aaba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25841 | ⟨a, b | ab=a, baba=abaa⟩ | φ(a) = a, φ(b) = b |