#998 ⟨a, b | ab=a, aab=ba⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 8
- 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:
-
b ⋅ a = a2 and a ⋅ a = a2, however b ≠ a
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:ab=a,aab=ba ab - -
ab=a
ba=aa
aaa=aa
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
33 total
| Σ | # | Presentation | Mapping |
|---|
| 8 | 1002 | ⟨a, b | ab=a, aba=ba⟩ | φ(a) = a, φ(b) = b |
| 8 | 1012 | ⟨a, b | ab=a, bab=aa⟩ | φ(a) = a, φ(b) = b |
| 9 | 3086 | ⟨a, b | ab=a, aabb=ba⟩ | φ(a) = a, φ(b) = b |
| 9 | 3094 | ⟨a, b | ab=a, abab=ba⟩ | φ(a) = a, φ(b) = b |
| 9 | 3098 | ⟨a, b | ab=a, abba=ba⟩ | φ(a) = a, φ(b) = b |
| 9 | 3116 | ⟨a, b | ab=a, babb=aa⟩ | φ(a) = a, φ(b) = b |
| 9 | 3183 | ⟨a, b | ab=a, bab=aab⟩ | φ(a) = a, φ(b) = b |
| 9 | 3184 | ⟨a, b | ab=a, bab=aba⟩ | φ(a) = a, φ(b) = b |
| 10 | 9014 | ⟨a, b | ab=a, aabbb=ba⟩ | φ(a) = a, φ(b) = b |
| 10 | 9030 | ⟨a, b | ab=a, ababb=ba⟩ | φ(a) = a, φ(b) = b |
| 10 | 9038 | ⟨a, b | ab=a, abbab=ba⟩ | φ(a) = a, φ(b) = b |
| 10 | 9042 | ⟨a, b | ab=a, abbba=ba⟩ | φ(a) = a, φ(b) = b |
| 10 | 9076 | ⟨a, b | ab=a, babbb=aa⟩ | φ(a) = a, φ(b) = b |
| 10 | 9285 | ⟨a, b | ab=a, aabb=bab⟩ | φ(a) = a, φ(b) = b |
| 10 | 9301 | ⟨a, b | ab=a, abab=bab⟩ | φ(a) = a, φ(b) = b |
| 10 | 9309 | ⟨a, b | ab=a, abba=bab⟩ | φ(a) = a, φ(b) = b |
| 10 | 9345 | ⟨a, b | ab=a, babb=aab⟩ | φ(a) = a, φ(b) = b |
| 10 | 9346 | ⟨a, b | ab=a, babb=aba⟩ | φ(a) = a, φ(b) = b |
| 11 | 24922 | ⟨a, b | ab=a, aabbbb=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 24954 | ⟨a, b | ab=a, ababbb=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 24970 | ⟨a, b | ab=a, abbabb=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 24978 | ⟨a, b | ab=a, abbbab=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 24982 | ⟨a, b | ab=a, abbbba=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25048 | ⟨a, b | ab=a, babbbb=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 25465 | ⟨a, b | ab=a, aabbb=bab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25497 | ⟨a, b | ab=a, ababb=bab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25513 | ⟨a, b | ab=a, abbab=bab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25521 | ⟨a, b | ab=a, abbba=bab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25589 | ⟨a, b | ab=a, babbb=aab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25590 | ⟨a, b | ab=a, babbb=aba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25850 | ⟨a, b | ab=a, babb=aabb⟩ | φ(a) = a, φ(b) = b |
| 11 | 25852 | ⟨a, b | ab=a, babb=abab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25853 | ⟨a, b | ab=a, babb=abba⟩ | φ(a) = a, φ(b) = b |