#259 ⟨a, b | ab=a, aaa=a⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 7
- 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:
-
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:ab=a,aaa=a ab - -
ab=a
aaa=a
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
105 total
| Σ | # | Presentation | Mapping |
|---|
| 8 | 922 | ⟨a, b | ab=a, aaab=a⟩ | φ(a) = a, φ(b) = b |
| 8 | 924 | ⟨a, b | ab=a, aaba=a⟩ | φ(a) = a, φ(b) = b |
| 8 | 928 | ⟨a, b | ab=a, abaa=a⟩ | φ(a) = a, φ(b) = b |
| 8 | 993 | ⟨a, b | ab=a, aaa=ab⟩ | φ(a) = a, φ(b) = b |
| 9 | 1982 | ⟨a, b | aaa=a, aaab=a⟩ | φ(a) = a, φ(b) = b |
| 9 | 2942 | ⟨a, b | ab=a, aaabb=a⟩ | φ(a) = a, φ(b) = b |
| 9 | 2946 | ⟨a, b | ab=a, aabab=a⟩ | φ(a) = a, φ(b) = b |
| 9 | 2948 | ⟨a, b | ab=a, aabba=a⟩ | φ(a) = a, φ(b) = b |
| 9 | 2954 | ⟨a, b | ab=a, abaab=a⟩ | φ(a) = a, φ(b) = b |
| 9 | 2956 | ⟨a, b | ab=a, ababa=a⟩ | φ(a) = a, φ(b) = b |
| 9 | 2960 | ⟨a, b | ab=a, abbaa=a⟩ | φ(a) = a, φ(b) = b |
| 9 | 3077 | ⟨a, b | ab=a, aaab=ab⟩ | φ(a) = a, φ(b) = b |
| 9 | 3081 | ⟨a, b | ab=a, aaba=ab⟩ | φ(a) = a, φ(b) = b |
| 9 | 3089 | ⟨a, b | ab=a, abaa=ab⟩ | φ(a) = a, φ(b) = b |
| 9 | 3175 | ⟨a, b | ab=a, abb=aaa⟩ | φ(a) = a, φ(b) = b |
| 10 | 5096 | ⟨a, b | aab=aa, aaab=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 5098 | ⟨a, b | aab=aa, aaba=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 5102 | ⟨a, b | aab=aa, abaa=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 5224 | ⟨a, b | aba=aa, aaab=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 5265 | ⟨a, b | aba=ab, babb=b⟩ | φ(a) = b, φ(b) = a |
| 10 | 5269 | ⟨a, b | aba=ab, bbab=b⟩ | φ(a) = b, φ(b) = a |
| 10 | 5271 | ⟨a, b | aba=ab, bbba=b⟩ | φ(a) = b, φ(b) = a |
| 10 | 8726 | ⟨a, b | ab=a, aaabbb=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 8734 | ⟨a, b | ab=a, aababb=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 8738 | ⟨a, b | ab=a, aabbab=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 8740 | ⟨a, b | ab=a, aabbba=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 8750 | ⟨a, b | ab=a, abaabb=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 8754 | ⟨a, b | ab=a, ababab=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 8756 | ⟨a, b | ab=a, ababba=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 8762 | ⟨a, b | ab=a, abbaab=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 8764 | ⟨a, b | ab=a, abbaba=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 8768 | ⟨a, b | ab=a, abbbaa=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 8997 | ⟨a, b | ab=a, aaabb=ab⟩ | φ(a) = a, φ(b) = b |
| 10 | 9005 | ⟨a, b | ab=a, aabab=ab⟩ | φ(a) = a, φ(b) = b |
| 10 | 9009 | ⟨a, b | ab=a, aabba=ab⟩ | φ(a) = a, φ(b) = b |
| 10 | 9021 | ⟨a, b | ab=a, abaab=ab⟩ | φ(a) = a, φ(b) = b |
| 10 | 9025 | ⟨a, b | ab=a, ababa=ab⟩ | φ(a) = a, φ(b) = b |
| 10 | 9033 | ⟨a, b | ab=a, abbaa=ab⟩ | φ(a) = a, φ(b) = b |
| 10 | 9267 | ⟨a, b | ab=a, aaab=abb⟩ | φ(a) = a, φ(b) = b |
| 10 | 9275 | ⟨a, b | ab=a, aaba=abb⟩ | φ(a) = a, φ(b) = b |
| 10 | 9291 | ⟨a, b | ab=a, abaa=abb⟩ | φ(a) = a, φ(b) = b |
| 10 | 9312 | ⟨a, b | ab=a, abbb=aaa⟩ | φ(a) = a, φ(b) = b |
| 11 | 12148 | ⟨a, b | aaaa=aa, aaab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 12354 | ⟨a, b | aaba=ab, abaa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 14415 | ⟨a, b | aaab=a, aaabb=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 14419 | ⟨a, b | aaab=a, aabab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 14421 | ⟨a, b | aaab=a, aabba=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 14427 | ⟨a, b | aaab=a, abaab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 14429 | ⟨a, b | aaab=a, ababa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 14433 | ⟨a, b | aaab=a, abbaa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 14547 | ⟨a, b | aaba=a, aabab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 14555 | ⟨a, b | aaba=a, abaab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 15551 | ⟨a, b | aab=aa, aaabb=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 15555 | ⟨a, b | aab=aa, aabab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 15557 | ⟨a, b | aab=aa, aabba=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 15563 | ⟨a, b | aab=aa, abaab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 15569 | ⟨a, b | aab=aa, abbaa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 15811 | ⟨a, b | aba=aa, aabab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 15817 | ⟨a, b | aba=aa, abaab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 15880 | ⟨a, b | aba=ab, baabb=b⟩ | φ(a) = b, φ(b) = a |
| 11 | 15884 | ⟨a, b | aba=ab, babab=b⟩ | φ(a) = b, φ(b) = a |
| 11 | 15886 | ⟨a, b | aba=ab, babba=b⟩ | φ(a) = b, φ(b) = a |
| 11 | 15892 | ⟨a, b | aba=ab, bbaab=b⟩ | φ(a) = b, φ(b) = a |
| 11 | 15894 | ⟨a, b | aba=ab, bbaba=b⟩ | φ(a) = b, φ(b) = a |
| 11 | 15898 | ⟨a, b | aba=ab, bbbaa=b⟩ | φ(a) = b, φ(b) = a |
| 11 | 18690 | ⟨a, b | aaa=a, aaaaab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 19233 | ⟨a, b | aaa=a, aaaaa=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 19235 | ⟨a, b | aaa=a, aaaab=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 19777 | ⟨a, b | aaa=a, aaaa=aab⟩ | φ(a) = a, φ(b) = b |
| 11 | 19782 | ⟨a, b | aaa=a, aaab=aaa⟩ | φ(a) = a, φ(b) = b |
| 11 | 24362 | ⟨a, b | ab=a, aaabbbb=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24378 | ⟨a, b | ab=a, aababbb=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24386 | ⟨a, b | ab=a, aabbabb=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24390 | ⟨a, b | ab=a, aabbbab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24392 | ⟨a, b | ab=a, aabbbba=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24410 | ⟨a, b | ab=a, abaabbb=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24418 | ⟨a, b | ab=a, abababb=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24422 | ⟨a, b | ab=a, ababbab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24424 | ⟨a, b | ab=a, ababbba=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24434 | ⟨a, b | ab=a, abbaabb=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24438 | ⟨a, b | ab=a, abbabab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24440 | ⟨a, b | ab=a, abbabba=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24446 | ⟨a, b | ab=a, abbbaab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24448 | ⟨a, b | ab=a, abbbaba=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24452 | ⟨a, b | ab=a, abbbbaa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24889 | ⟨a, b | ab=a, aaabbb=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 24905 | ⟨a, b | ab=a, aababb=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 24913 | ⟨a, b | ab=a, aabbab=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 24917 | ⟨a, b | ab=a, aabbba=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 24937 | ⟨a, b | ab=a, abaabb=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 24945 | ⟨a, b | ab=a, ababab=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 24949 | ⟨a, b | ab=a, ababba=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 24961 | ⟨a, b | ab=a, abbaab=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 24965 | ⟨a, b | ab=a, abbaba=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 24973 | ⟨a, b | ab=a, abbbaa=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25431 | ⟨a, b | ab=a, aaabb=abb⟩ | φ(a) = a, φ(b) = b |
| 11 | 25447 | ⟨a, b | ab=a, aabab=abb⟩ | φ(a) = a, φ(b) = b |
| 11 | 25455 | ⟨a, b | ab=a, aabba=abb⟩ | φ(a) = a, φ(b) = b |
| 11 | 25479 | ⟨a, b | ab=a, abaab=abb⟩ | φ(a) = a, φ(b) = b |
| 11 | 25487 | ⟨a, b | ab=a, ababa=abb⟩ | φ(a) = a, φ(b) = b |
| 11 | 25503 | ⟨a, b | ab=a, abbaa=abb⟩ | φ(a) = a, φ(b) = b |
| 11 | 25524 | ⟨a, b | ab=a, abbbb=aaa⟩ | φ(a) = a, φ(b) = b |
| 11 | 25814 | ⟨a, b | ab=a, abbb=aaab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25815 | ⟨a, b | ab=a, abbb=aaba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25817 | ⟨a, b | ab=a, abbb=abaa⟩ | φ(a) = a, φ(b) = b |