#1988 ⟨a, b | aaa=a, abab=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 ⋅ a2 = a and a ⋅ 1 = a, however a2 ≠ 1
- Not right cancellative, because right multiplication by a is not injective:
-
a2 ⋅ a = a and 1 ⋅ a = a, however a2 ≠ 1
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aaa=a,abab=a ab - -
aaa=a
aba=aab
abb=aa
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
12 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 12154 | ⟨a, b | aaaa=aa, abab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 12248 | ⟨a, b | aaab=ab, abab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 12352 | ⟨a, b | aaba=ab, aabb=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 12356 | ⟨a, b | aaba=ab, abab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 12358 | ⟨a, b | aaba=ab, abba=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 14759 | ⟨a, b | abab=a, abbbb=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 18698 | ⟨a, b | aaa=a, aaabab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 18704 | ⟨a, b | aaa=a, aabaab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 18718 | ⟨a, b | aaa=a, abaaab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 19250 | ⟨a, b | aaa=a, aabab=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 19262 | ⟨a, b | aaa=a, abaab=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 19806 | ⟨a, b | aaa=a, abab=aaa⟩ | φ(a) = a, φ(b) = b |