#2176 ⟨a, b | ab=aa, aaaa=a⟩
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 = a2 and a ⋅ a = a2, however b ≠ a
- Not right cancellative, because right multiplication by a is not injective:
-
a3 ⋅ a = a and 1 ⋅ a = a, however a3 ≠ 1
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:ab=aa,aaaa=a ab - -
ab=aa
aaaa=a
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
32 total
| Σ | # | Presentation | Mapping |
|---|
| 9 | 2178 | ⟨a, b | ab=aa, aaab=a⟩ | φ(a) = a, φ(b) = b |
| 9 | 2180 | ⟨a, b | ab=aa, aaba=a⟩ | φ(a) = a, φ(b) = b |
| 9 | 2182 | ⟨a, b | ab=aa, aabb=a⟩ | φ(a) = a, φ(b) = b |
| 9 | 2184 | ⟨a, b | ab=aa, abaa=a⟩ | φ(a) = a, φ(b) = b |
| 9 | 2186 | ⟨a, b | ab=aa, abab=a⟩ | φ(a) = a, φ(b) = b |
| 9 | 2188 | ⟨a, b | ab=aa, abba=a⟩ | φ(a) = a, φ(b) = b |
| 9 | 2190 | ⟨a, b | ab=aa, abbb=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 4614 | ⟨a, b | aaaa=a, aaab=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 4651 | ⟨a, b | aaab=a, aabb=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 4655 | ⟨a, b | aaab=a, abab=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 4657 | ⟨a, b | aaab=a, abba=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 4702 | ⟨a, b | aaba=a, abab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 12880 | ⟨a, b | aab=aaa, aaaa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 12882 | ⟨a, b | aab=aaa, aaab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 12884 | ⟨a, b | aab=aaa, aaba=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 12886 | ⟨a, b | aab=aaa, aabb=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 12888 | ⟨a, b | aab=aaa, abaa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 12890 | ⟨a, b | aab=aaa, abab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 12914 | ⟨a, b | aba=aaa, aaab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 12920 | ⟨a, b | aba=aaa, abab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 12998 | ⟨a, b | abb=aab, aaab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 13002 | ⟨a, b | abb=aab, aabb=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 13005 | ⟨a, b | abb=aab, abab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 13014 | ⟨a, b | abb=aba, aaab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 13022 | ⟨a, b | abb=aba, abab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 13026 | ⟨a, b | abb=aba, abbb=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 13031 | ⟨a, b | abb=aba, baab=b⟩ | φ(a) = b, φ(b) = a |
| 11 | 13033 | ⟨a, b | abb=aba, baba=b⟩ | φ(a) = b, φ(b) = a |
| 11 | 13035 | ⟨a, b | abb=aba, babb=b⟩ | φ(a) = b, φ(b) = a |
| 11 | 13037 | ⟨a, b | abb=aba, bbaa=b⟩ | φ(a) = b, φ(b) = a |
| 11 | 13039 | ⟨a, b | abb=aba, bbab=b⟩ | φ(a) = b, φ(b) = a |
| 11 | 13041 | ⟨a, b | abb=aba, bbba=b⟩ | φ(a) = b, φ(b) = a |