#563 ⟨a, b | aaa=a, aab=a⟩
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 ⋅ 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,aab=a ab - -
ab=aa
aaa=a
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
35 total
| Σ | # | Presentation | Mapping |
|---|
| 8 | 584 | ⟨a, b | aab=a, abb=a⟩ | φ(a) = a, φ(b) = b |
| 8 | 630 | ⟨a, b | ab=aa, aaa=a⟩ | φ(a) = a, φ(b) = b |
| 8 | 632 | ⟨a, b | ab=aa, aab=a⟩ | φ(a) = a, φ(b) = b |
| 8 | 634 | ⟨a, b | ab=aa, aba=a⟩ | φ(a) = a, φ(b) = b |
| 8 | 636 | ⟨a, b | ab=aa, abb=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 4167 | ⟨a, b | abb=aba, bab=b⟩ | φ(a) = b, φ(b) = a |
| 10 | 4169 | ⟨a, b | abb=aba, bba=b⟩ | φ(a) = b, φ(b) = a |
| 10 | 4197 | ⟨a, b | bab=baa, bba=b⟩ | φ(a) = b, φ(b) = a |
| 10 | 6240 | ⟨a, b | aaa=a, aaaab=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 6320 | ⟨a, b | aab=a, aaaab=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 6322 | ⟨a, b | aab=a, aaaba=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 6326 | ⟨a, b | aab=a, aabaa=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 6332 | ⟨a, b | aab=a, aabbb=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 6334 | ⟨a, b | aab=a, abaaa=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 6340 | ⟨a, b | aab=a, ababb=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 6344 | ⟨a, b | aab=a, abbab=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 6346 | ⟨a, b | aab=a, abbba=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 6448 | ⟨a, b | aba=a, aaaab=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 6468 | ⟨a, b | aba=a, abbab=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 6527 | ⟨a, b | aaa=a, aaaa=ab⟩ | φ(a) = a, φ(b) = b |
| 10 | 6529 | ⟨a, b | aaa=a, aaab=aa⟩ | φ(a) = a, φ(b) = b |
| 10 | 6598 | ⟨a, b | aab=a, aaaa=aa⟩ | φ(a) = a, φ(b) = b |
| 10 | 6603 | ⟨a, b | aab=a, aaab=ab⟩ | φ(a) = a, φ(b) = b |
| 10 | 6607 | ⟨a, b | aab=a, aaba=ab⟩ | φ(a) = a, φ(b) = b |
| 10 | 6610 | ⟨a, b | aab=a, aabb=aa⟩ | φ(a) = a, φ(b) = b |
| 10 | 6615 | ⟨a, b | aab=a, abaa=ab⟩ | φ(a) = a, φ(b) = b |
| 10 | 6618 | ⟨a, b | aab=a, abab=aa⟩ | φ(a) = a, φ(b) = b |
| 10 | 6622 | ⟨a, b | aab=a, abba=aa⟩ | φ(a) = a, φ(b) = b |
| 10 | 6627 | ⟨a, b | aab=a, abbb=ab⟩ | φ(a) = a, φ(b) = b |
| 10 | 6632 | ⟨a, b | aab=a, baaa=ba⟩ | φ(a) = a, φ(b) = b |
| 10 | 6644 | ⟨a, b | aab=a, babb=ba⟩ | φ(a) = a, φ(b) = b |
| 10 | 6734 | ⟨a, b | aba=a, aaba=ab⟩ | φ(a) = a, φ(b) = b |
| 10 | 6741 | ⟨a, b | aba=a, abab=aa⟩ | φ(a) = a, φ(b) = b |
| 10 | 6798 | ⟨a, b | aaa=a, aab=aaa⟩ | φ(a) = a, φ(b) = b |
| 10 | 6810 | ⟨a, b | aab=a, abb=aab⟩ | φ(a) = a, φ(b) = b |