#20920 ⟨a, b | ab=aa, aaaa=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:
-
a3 ⋅ a = a3 and a2 ⋅ a = a3, however a3 ≠ a2
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:ab=aa,aaaa=aaa ab - -
ab=aa
aaaa=aaa
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
31 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 20921 | ⟨a, b | ab=aa, aaaa=aab⟩ | φ(a) = a, φ(b) = b |
| 11 | 20922 | ⟨a, b | ab=aa, aaaa=aba⟩ | φ(a) = a, φ(b) = b |
| 11 | 20923 | ⟨a, b | ab=aa, aaaa=abb⟩ | φ(a) = a, φ(b) = b |
| 11 | 20928 | ⟨a, b | ab=aa, aaab=aaa⟩ | φ(a) = a, φ(b) = b |
| 11 | 20929 | ⟨a, b | ab=aa, aaab=aab⟩ | φ(a) = a, φ(b) = b |
| 11 | 20930 | ⟨a, b | ab=aa, aaab=aba⟩ | φ(a) = a, φ(b) = b |
| 11 | 20931 | ⟨a, b | ab=aa, aaab=abb⟩ | φ(a) = a, φ(b) = b |
| 11 | 20936 | ⟨a, b | ab=aa, aaba=aaa⟩ | φ(a) = a, φ(b) = b |
| 11 | 20937 | ⟨a, b | ab=aa, aaba=aab⟩ | φ(a) = a, φ(b) = b |
| 11 | 20938 | ⟨a, b | ab=aa, aaba=aba⟩ | φ(a) = a, φ(b) = b |
| 11 | 20939 | ⟨a, b | ab=aa, aaba=abb⟩ | φ(a) = a, φ(b) = b |
| 11 | 20944 | ⟨a, b | ab=aa, aabb=aaa⟩ | φ(a) = a, φ(b) = b |
| 11 | 20945 | ⟨a, b | ab=aa, aabb=aab⟩ | φ(a) = a, φ(b) = b |
| 11 | 20946 | ⟨a, b | ab=aa, aabb=aba⟩ | φ(a) = a, φ(b) = b |
| 11 | 20947 | ⟨a, b | ab=aa, aabb=abb⟩ | φ(a) = a, φ(b) = b |
| 11 | 20952 | ⟨a, b | ab=aa, abaa=aaa⟩ | φ(a) = a, φ(b) = b |
| 11 | 20953 | ⟨a, b | ab=aa, abaa=aab⟩ | φ(a) = a, φ(b) = b |
| 11 | 20954 | ⟨a, b | ab=aa, abaa=aba⟩ | φ(a) = a, φ(b) = b |
| 11 | 20955 | ⟨a, b | ab=aa, abaa=abb⟩ | φ(a) = a, φ(b) = b |
| 11 | 20960 | ⟨a, b | ab=aa, abab=aaa⟩ | φ(a) = a, φ(b) = b |
| 11 | 20961 | ⟨a, b | ab=aa, abab=aab⟩ | φ(a) = a, φ(b) = b |
| 11 | 20962 | ⟨a, b | ab=aa, abab=aba⟩ | φ(a) = a, φ(b) = b |
| 11 | 20963 | ⟨a, b | ab=aa, abab=abb⟩ | φ(a) = a, φ(b) = b |
| 11 | 20968 | ⟨a, b | ab=aa, abba=aaa⟩ | φ(a) = a, φ(b) = b |
| 11 | 20969 | ⟨a, b | ab=aa, abba=aab⟩ | φ(a) = a, φ(b) = b |
| 11 | 20970 | ⟨a, b | ab=aa, abba=aba⟩ | φ(a) = a, φ(b) = b |
| 11 | 20971 | ⟨a, b | ab=aa, abba=abb⟩ | φ(a) = a, φ(b) = b |
| 11 | 20976 | ⟨a, b | ab=aa, abbb=aaa⟩ | φ(a) = a, φ(b) = b |
| 11 | 20977 | ⟨a, b | ab=aa, abbb=aab⟩ | φ(a) = a, φ(b) = b |
| 11 | 20978 | ⟨a, b | ab=aa, abbb=aba⟩ | φ(a) = a, φ(b) = b |
| 11 | 20979 | ⟨a, b | ab=aa, abbb=abb⟩ | φ(a) = a, φ(b) = b |