#239 ⟨a, b | aa=a, aba=a⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 7
- Infinite non-cancellative non-commutative monoid
- Element ab2 has infinite order
- Not left cancellative, because left multiplication by a is not injective:
-
a ⋅ a = a and a ⋅ 1 = a, however a ≠ 1
- Not right cancellative, because right multiplication by a is not injective:
-
a ⋅ a = a and 1 ⋅ a = a, however a ≠ 1
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aa=a,aba=a ab - -
aa=a
aba=a
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
45 total
| Σ | # | Presentation | Mapping |
|---|
| 8 | 884 | ⟨a, b | aa=a, aaba=a⟩ | φ(a) = a, φ(b) = b |
| 8 | 959 | ⟨a, b | aa=a, aba=aa⟩ | φ(a) = a, φ(b) = b |
| 9 | 1622 | ⟨a, b | aab=ab, aba=a⟩ | φ(a) = a, φ(b) = b |
| 9 | 2088 | ⟨a, b | aba=a, aaba=a⟩ | φ(a) = a, φ(b) = b |
| 9 | 2860 | ⟨a, b | aa=a, aaaba=a⟩ | φ(a) = a, φ(b) = b |
| 9 | 2864 | ⟨a, b | aa=a, aabaa=a⟩ | φ(a) = a, φ(b) = b |
| 9 | 3007 | ⟨a, b | aa=a, aaba=aa⟩ | φ(a) = a, φ(b) = b |
| 9 | 3137 | ⟨a, b | aa=a, aba=aaa⟩ | φ(a) = a, φ(b) = b |
| 10 | 5026 | ⟨a, b | aaa=aa, aaba=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 5130 | ⟨a, b | aab=ab, aaba=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 5134 | ⟨a, b | aab=ab, abaa=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 8572 | ⟨a, b | aa=a, aaaaba=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 8576 | ⟨a, b | aa=a, aaabaa=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 8847 | ⟨a, b | aa=a, aaaba=aa⟩ | φ(a) = a, φ(b) = b |
| 10 | 8855 | ⟨a, b | aa=a, aabaa=aa⟩ | φ(a) = a, φ(b) = b |
| 10 | 9114 | ⟨a, b | aa=a, aaaa=aba⟩ | φ(a) = a, φ(b) = b |
| 10 | 9126 | ⟨a, b | aa=a, aaba=aaa⟩ | φ(a) = a, φ(b) = b |
| 11 | 12328 | ⟨a, b | aaba=aa, abaa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 12526 | ⟨a, b | abab=ab, babb=b⟩ | φ(a) = b, φ(b) = a |
| 11 | 12529 | ⟨a, b | abab=ab, bbab=b⟩ | φ(a) = b, φ(b) = a |
| 11 | 14541 | ⟨a, b | aaba=a, aaaba=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 14545 | ⟨a, b | aaba=a, aabaa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 14553 | ⟨a, b | aaba=a, abaaa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 15405 | ⟨a, b | aaa=aa, aaaba=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 15409 | ⟨a, b | aaa=aa, aabaa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 15613 | ⟨a, b | aab=ab, aaaba=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 15617 | ⟨a, b | aab=ab, aabaa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 15625 | ⟨a, b | aab=ab, abaaa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 19106 | ⟨a, b | aba=a, aababa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 19120 | ⟨a, b | aba=a, abaaba=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 19651 | ⟨a, b | aba=a, aabab=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 19663 | ⟨a, b | aba=a, abaab=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 19666 | ⟨a, b | aba=a, ababa=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 20192 | ⟨a, b | aba=a, aaba=aba⟩ | φ(a) = a, φ(b) = b |
| 11 | 20207 | ⟨a, b | aba=a, abab=aab⟩ | φ(a) = a, φ(b) = b |
| 11 | 20232 | ⟨a, b | aba=a, baab=bab⟩ | φ(a) = a, φ(b) = b |
| 11 | 24048 | ⟨a, b | aa=a, aaaaaba=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24052 | ⟨a, b | aa=a, aaaabaa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24060 | ⟨a, b | aa=a, aaabaaa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24595 | ⟨a, b | aa=a, aaaaba=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 24603 | ⟨a, b | aa=a, aaabaa=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 25118 | ⟨a, b | aa=a, aaaaa=aba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25130 | ⟨a, b | aa=a, aaaba=aaa⟩ | φ(a) = a, φ(b) = b |
| 11 | 25146 | ⟨a, b | aa=a, aabaa=aaa⟩ | φ(a) = a, φ(b) = b |
| 11 | 25661 | ⟨a, b | aa=a, aaba=aaaa⟩ | φ(a) = a, φ(b) = b |