#20984 ⟨a, b | ab=aa, baaa=aaa⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 11
- Infinite non-cancellative non-commutative monoid
- Element b has infinite order
- Not left cancellative, because left multiplication by a is not injective:
-
a ⋅ b = a2 and a ⋅ a = a2, however b ≠ a
- Not right cancellative, because right multiplication by a is not injective:
-
ba2 ⋅ a = a3 and a2 ⋅ a = a3, however ba2 ≠ a2
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:ab=aa,baaa=aaa ab - -
ab=aa
baaa=aaa
aaaaa=aaaa
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
15 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 20985 | ⟨a, b | ab=aa, baaa=aab⟩ | φ(a) = a, φ(b) = b |
| 11 | 20986 | ⟨a, b | ab=aa, baaa=aba⟩ | φ(a) = a, φ(b) = b |
| 11 | 20987 | ⟨a, b | ab=aa, baaa=abb⟩ | φ(a) = a, φ(b) = b |
| 11 | 20992 | ⟨a, b | ab=aa, baab=aaa⟩ | φ(a) = a, φ(b) = b |
| 11 | 20993 | ⟨a, b | ab=aa, baab=aab⟩ | φ(a) = a, φ(b) = b |
| 11 | 20994 | ⟨a, b | ab=aa, baab=aba⟩ | φ(a) = a, φ(b) = b |
| 11 | 20995 | ⟨a, b | ab=aa, baab=abb⟩ | φ(a) = a, φ(b) = b |
| 11 | 21000 | ⟨a, b | ab=aa, baba=aaa⟩ | φ(a) = a, φ(b) = b |
| 11 | 21001 | ⟨a, b | ab=aa, baba=aab⟩ | φ(a) = a, φ(b) = b |
| 11 | 21002 | ⟨a, b | ab=aa, baba=aba⟩ | φ(a) = a, φ(b) = b |
| 11 | 21003 | ⟨a, b | ab=aa, baba=abb⟩ | φ(a) = a, φ(b) = b |
| 11 | 21008 | ⟨a, b | ab=aa, babb=aaa⟩ | φ(a) = a, φ(b) = b |
| 11 | 21009 | ⟨a, b | ab=aa, babb=aab⟩ | φ(a) = a, φ(b) = b |
| 11 | 21010 | ⟨a, b | ab=aa, babb=aba⟩ | φ(a) = a, φ(b) = b |
| 11 | 21011 | ⟨a, b | ab=aa, babb=abb⟩ | φ(a) = a, φ(b) = b |