#20720 ⟨a, b | ab=aa, aaaaa=aa⟩
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:
-
a4 ⋅ a = a2 and a ⋅ a = a2, however a4 ≠ a
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:ab=aa,aaaaa=aa ab - -
ab=aa
aaaaa=aa
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
31 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 20721 | ⟨a, b | ab=aa, aaaaa=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 20724 | ⟨a, b | ab=aa, aaaab=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 20725 | ⟨a, b | ab=aa, aaaab=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 20728 | ⟨a, b | ab=aa, aaaba=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 20729 | ⟨a, b | ab=aa, aaaba=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 20732 | ⟨a, b | ab=aa, aaabb=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 20733 | ⟨a, b | ab=aa, aaabb=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 20736 | ⟨a, b | ab=aa, aabaa=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 20737 | ⟨a, b | ab=aa, aabaa=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 20740 | ⟨a, b | ab=aa, aabab=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 20741 | ⟨a, b | ab=aa, aabab=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 20744 | ⟨a, b | ab=aa, aabba=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 20745 | ⟨a, b | ab=aa, aabba=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 20748 | ⟨a, b | ab=aa, aabbb=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 20749 | ⟨a, b | ab=aa, aabbb=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 20752 | ⟨a, b | ab=aa, abaaa=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 20753 | ⟨a, b | ab=aa, abaaa=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 20756 | ⟨a, b | ab=aa, abaab=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 20757 | ⟨a, b | ab=aa, abaab=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 20760 | ⟨a, b | ab=aa, ababa=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 20761 | ⟨a, b | ab=aa, ababa=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 20764 | ⟨a, b | ab=aa, ababb=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 20765 | ⟨a, b | ab=aa, ababb=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 20768 | ⟨a, b | ab=aa, abbaa=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 20769 | ⟨a, b | ab=aa, abbaa=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 20772 | ⟨a, b | ab=aa, abbab=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 20773 | ⟨a, b | ab=aa, abbab=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 20776 | ⟨a, b | ab=aa, abbba=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 20777 | ⟨a, b | ab=aa, abbba=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 20780 | ⟨a, b | ab=aa, abbbb=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 20781 | ⟨a, b | ab=aa, abbbb=ab⟩ | φ(a) = a, φ(b) = b |