#920 ⟨a, b | ab=a, aaaa=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 ⋅ b = a and a ⋅ 1 = a, however b ≠ 1
- 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=a,aaaa=a ab - -
ab=a
aaaa=a
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
66 total
| Σ | # | Presentation | Mapping |
|---|
| 9 | 2938 | ⟨a, b | ab=a, aaaab=a⟩ | φ(a) = a, φ(b) = b |
| 9 | 2940 | ⟨a, b | ab=a, aaaba=a⟩ | φ(a) = a, φ(b) = b |
| 9 | 2944 | ⟨a, b | ab=a, aabaa=a⟩ | φ(a) = a, φ(b) = b |
| 9 | 2952 | ⟨a, b | ab=a, abaaa=a⟩ | φ(a) = a, φ(b) = b |
| 9 | 3073 | ⟨a, b | ab=a, aaaa=ab⟩ | φ(a) = a, φ(b) = b |
| 10 | 5094 | ⟨a, b | aab=aa, aaaa=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 8718 | ⟨a, b | ab=a, aaaabb=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 8722 | ⟨a, b | ab=a, aaabab=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 8724 | ⟨a, b | ab=a, aaabba=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 8730 | ⟨a, b | ab=a, aabaab=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 8732 | ⟨a, b | ab=a, aababa=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 8736 | ⟨a, b | ab=a, aabbaa=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 8746 | ⟨a, b | ab=a, abaaab=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 8748 | ⟨a, b | ab=a, abaaba=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 8752 | ⟨a, b | ab=a, ababaa=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 8760 | ⟨a, b | ab=a, abbaaa=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 8989 | ⟨a, b | ab=a, aaaab=ab⟩ | φ(a) = a, φ(b) = b |
| 10 | 8993 | ⟨a, b | ab=a, aaaba=ab⟩ | φ(a) = a, φ(b) = b |
| 10 | 9001 | ⟨a, b | ab=a, aabaa=ab⟩ | φ(a) = a, φ(b) = b |
| 10 | 9017 | ⟨a, b | ab=a, abaaa=ab⟩ | φ(a) = a, φ(b) = b |
| 10 | 9259 | ⟨a, b | ab=a, aaaa=abb⟩ | φ(a) = a, φ(b) = b |
| 11 | 14331 | ⟨a, b | aaaa=a, aaaab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 15547 | ⟨a, b | aab=aa, aaaab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 15549 | ⟨a, b | aab=aa, aaaba=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 15553 | ⟨a, b | aab=aa, aabaa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 15561 | ⟨a, b | aab=aa, abaaa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 15803 | ⟨a, b | aba=aa, aaaab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 15888 | ⟨a, b | aba=ab, babbb=b⟩ | φ(a) = b, φ(b) = a |
| 11 | 15896 | ⟨a, b | aba=ab, bbabb=b⟩ | φ(a) = b, φ(b) = a |
| 11 | 15900 | ⟨a, b | aba=ab, bbbab=b⟩ | φ(a) = b, φ(b) = a |
| 11 | 15902 | ⟨a, b | aba=ab, bbbba=b⟩ | φ(a) = b, φ(b) = a |
| 11 | 24346 | ⟨a, b | ab=a, aaaabbb=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24354 | ⟨a, b | ab=a, aaababb=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24358 | ⟨a, b | ab=a, aaabbab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24360 | ⟨a, b | ab=a, aaabbba=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24370 | ⟨a, b | ab=a, aabaabb=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24374 | ⟨a, b | ab=a, aababab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24376 | ⟨a, b | ab=a, aababba=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24382 | ⟨a, b | ab=a, aabbaab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24384 | ⟨a, b | ab=a, aabbaba=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24388 | ⟨a, b | ab=a, aabbbaa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24402 | ⟨a, b | ab=a, abaaabb=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24406 | ⟨a, b | ab=a, abaabab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24408 | ⟨a, b | ab=a, abaabba=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24414 | ⟨a, b | ab=a, ababaab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24416 | ⟨a, b | ab=a, abababa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24420 | ⟨a, b | ab=a, ababbaa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24430 | ⟨a, b | ab=a, abbaaab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24432 | ⟨a, b | ab=a, abbaaba=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24436 | ⟨a, b | ab=a, abbabaa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24444 | ⟨a, b | ab=a, abbbaaa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24873 | ⟨a, b | ab=a, aaaabb=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 24881 | ⟨a, b | ab=a, aaabab=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 24885 | ⟨a, b | ab=a, aaabba=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 24897 | ⟨a, b | ab=a, aabaab=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 24901 | ⟨a, b | ab=a, aababa=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 24909 | ⟨a, b | ab=a, aabbaa=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 24929 | ⟨a, b | ab=a, abaaab=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 24933 | ⟨a, b | ab=a, abaaba=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 24941 | ⟨a, b | ab=a, ababaa=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 24957 | ⟨a, b | ab=a, abbaaa=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25415 | ⟨a, b | ab=a, aaaab=abb⟩ | φ(a) = a, φ(b) = b |
| 11 | 25423 | ⟨a, b | ab=a, aaaba=abb⟩ | φ(a) = a, φ(b) = b |
| 11 | 25439 | ⟨a, b | ab=a, aabaa=abb⟩ | φ(a) = a, φ(b) = b |
| 11 | 25471 | ⟨a, b | ab=a, abaaa=abb⟩ | φ(a) = a, φ(b) = b |
| 11 | 25813 | ⟨a, b | ab=a, abbb=aaaa⟩ | φ(a) = a, φ(b) = b |