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〈a, b | aaaa=b, abbb=1〉

Monoid presentation of length 9

Properties

Completion parameters

Inverses of generators

Complete rewriting system

  1. a13 ⇒ 1
  2. b ⇒ a4

Cayley table

1aa2a3a4a5a6a7a8a9a10a11a12
11aa2a3a4a5a6a7a8a9a10a11a12
aaa2a3a4a5a6a7a8a9a10a11a121
a2a2a3a4a5a6a7a8a9a10a11a121a
a3a3a4a5a6a7a8a9a10a11a121aa2
a4a4a5a6a7a8a9a10a11a121aa2a3
a5a5a6a7a8a9a10a11a121aa2a3a4
a6a6a7a8a9a10a11a121aa2a3a4a5
a7a7a8a9a10a11a121aa2a3a4a5a6
a8a8a9a10a11a121aa2a3a4a5a6a7
a9a9a10a11a121aa2a3a4a5a6a7a8
a10a10a11a121aa2a3a4a5a6a7a8a9
a11a11a121aa2a3a4a5a6a7a8a9a10
a12a121aa2a3a4a5a6a7a8a9a10a11

Right Cayley graph

Others with same cardinality

33 unique, 114 total

Length:Presentation:Description:Related:
9 〈a, b | aba=b, baab=a〉 Finite non-commutative monoid with 13 elements 4 isomorphic
10 〈a, b | aaaa=b, abbb=a〉 Finite commutative monoid with 13 elements 10 isomorphic
10 〈a, b | aaaa=b, abbb=b〉 Finite commutative monoid with 13 elements 6 isomorphic
10 〈a, b | aaab=b, abba=a〉 Finite non-commutative monoid with 13 elements 2 isomorphic
10 〈a, b | aaa=ab, babb=b〉 Finite non-commutative monoid with 13 elements 6 isomorphic
10 〈a, b | aaa=ab, bba=bb〉 Finite non-commutative monoid with 13 elements
10 〈a, b | aaa=ab, bbb=ab〉 Finite non-commutative monoid with 13 elements 1 isomorphic
10 〈a, b | aaa=ab, bbb=ba〉 Finite non-commutative monoid with 13 elements
10 〈a, b | aaa=bb, aab=ba〉 Finite non-commutative monoid with 13 elements
10 〈a, b | aaa=b, abbbb=b〉 Finite commutative monoid with 13 elements 2 isomorphic
10 〈a, b | aab=b, abbba=a〉 Finite non-commutative monoid with 13 elements 3 isomorphic
10 〈a, b | bb=aa, aaab=ba〉 Finite non-commutative monoid with 13 elements 1 isomorphic
11 〈a, b | aaab=aa, bbbb=a〉 Finite commutative monoid with 13 elements 1 isomorphic
11 〈a, b | aaab=ab, bbbb=a〉 Finite commutative monoid with 13 elements 3 isomorphic
11 〈a, b | aaab=bb, bbbb=a〉 Finite commutative monoid with 13 elements 14 isomorphic
11 〈a, b | aaab=b, aabba=a〉 Finite non-commutative monoid with 13 elements 3 isomorphic
11 〈a, b | aaba=b, babbb=a〉 Finite commutative monoid with 13 elements 2 isomorphic
11 〈a, b | aaa=bb, aabbb=b〉 Finite commutative monoid with 13 elements 2 isomorphic
11 〈a, b | aaa=ab, abbb=bb〉 Finite non-commutative monoid with 13 elements
11 〈a, b | aaa=bb, abbb=ba〉 Finite non-commutative monoid with 13 elements
11 〈a, b | aaa=bb, babb=ab〉 Finite non-commutative monoid with 13 elements
11 〈a, b | aab=ab, bbbb=aa〉 Finite non-commutative monoid with 13 elements 1 isomorphic
11 〈a, b | aab=ba, bbbb=aa〉 Finite non-commutative monoid with 13 elements
11 〈a, b | aba=bb, abbb=aa〉 Finite non-commutative monoid with 13 elements 1 isomorphic
11 〈a, b | aab=ab, bbb=aaa〉 Finite non-commutative monoid with 13 elements 1 isomorphic
11 〈a, b | aab=ba, bbb=aaa〉 Finite non-commutative monoid with 13 elements
11 〈a, b | aab=a, bbbbbb=a〉 Finite commutative monoid with 13 elements 4 isomorphic
11 〈a, b | aab=b, ababba=a〉 Finite non-commutative monoid with 13 elements 4 isomorphic
11 〈a, b | aab=a, baaa=bbb〉 Finite non-commutative monoid with 13 elements
11 〈a, b | aab=a, bbbb=bba〉 Finite non-commutative monoid with 13 elements
11 〈a, b | ab=aa, aaaa=bbb〉 Finite non-commutative monoid with 13 elements 7 isomorphic
11 〈a, b | ab=aa, baaa=bbb〉 Finite non-commutative monoid with 13 elements 3 isomorphic
11 〈a, b | ab=a, baaaaaa=b〉 Finite non-commutative monoid with 13 elements

Other isomorphic instances

189 total

Length:Presentation:
9〈a, b | aaaa=b, babb=1〉
9〈a, b | aaa=b, abbbb=1〉
9〈a, b | aaa=b, babbb=1〉
9〈a, b | aaa=b, bbabb=1〉
10〈a, b | aaa=bb, aabbb=1〉
10〈a, b | aaa=bb, ababb=1〉
10〈a, b | aaa=bb, abbab=1〉
10〈a, b | aaa=bb, abbba=1〉
10〈a, b | aaa=bb, baabb=1〉
10〈a, b | aaa=bb, babab=1〉
10〈a, b | aab=1, bbbbbb=a〉
10〈a, b | aba=1, bbbbbb=a〉
10〈a, b | aa=b, abbbbbb=1〉
10〈a, b | aa=b, babbbbb=1〉
10〈a, b | aa=b, bbabbbb=1〉
10〈a, b | aa=b, bbbabbb=1〉
11〈a, b | aaaa=bbb, aaab=1〉
11〈a, b | aaaa=bbb, aaba=1〉
11〈a, b | aaaaa=b, aaabb=1〉
11〈a, b | aaaaa=b, aabab=1〉
11〈a, b | aaaaa=b, aabba=1〉
11〈a, b | aaaaa=b, abaab=1〉
11〈a, b | aaaaa=b, ababa=1〉
11〈a, b | aaaaa=b, baaab=1〉
11〈a, b | aaaa=ab, abbbb=1〉
11〈a, b | aaaa=ab, babbb=1〉
11〈a, b | aaaa=ab, bbabb=1〉
11〈a, b | aaaa=ab, bbbab=1〉
11〈a, b | aaaa=ab, bbbba=1〉
11〈a, b | aaab=bb, abbbb=1〉
11〈a, b | aaab=bb, babbb=1〉
11〈a, b | aaab=bb, bbabb=1〉
11〈a, b | aaab=bb, bbbab=1〉
11〈a, b | aaab=bb, bbbba=1〉
11〈a, b | aaba=bb, abbbb=1〉
11〈a, b | aaba=bb, babbb=1〉
11〈a, b | aaba=bb, bbabb=1〉
11〈a, b | aaba=bb, bbbab=1〉
11〈a, b | aaba=bb, bbbba=1〉
11〈a, b | aaabb=1, abbbbb=1〉
11〈a, b | aaabb=1, babbbb=1〉
11〈a, b | aaabb=1, bbabbb=1〉
11〈a, b | aaabb=1, bbbabb=1〉
11〈a, b | aaabb=1, bbbbab=1〉
11〈a, b | aaabb=1, bbbbba=1〉
11〈a, b | aabab=1, abbbbb=1〉
11〈a, b | aabab=1, babbbb=1〉
11〈a, b | aabab=1, bbabbb=1〉
11〈a, b | aabab=1, bbbabb=1〉
11〈a, b | aabab=1, bbbbab=1〉
11〈a, b | aabab=1, bbbbba=1〉
11〈a, b | aabba=1, abbbbb=1〉
11〈a, b | aabba=1, babbbb=1〉
11〈a, b | aabba=1, bbabbb=1〉
11〈a, b | aabba=1, bbbabb=1〉
11〈a, b | aabba=1, bbbbab=1〉
11〈a, b | aabba=1, bbbbba=1〉
11〈a, b | abaab=1, abbbbb=1〉
11〈a, b | abaab=1, babbbb=1〉
11〈a, b | abaab=1, bbabbb=1〉
11〈a, b | abaab=1, bbbabb=1〉
11〈a, b | abaab=1, bbbbab=1〉
11〈a, b | abaab=1, bbbbba=1〉
11〈a, b | ababa=1, abbbbb=1〉
11〈a, b | ababa=1, babbbb=1〉
11〈a, b | ababa=1, bbabbb=1〉
11〈a, b | abbba=1, aaaaab=1〉
11〈a, b | abbba=1, aaaaba=1〉
11〈a, b | abbba=1, aaabaa=1〉
11〈a, b | aaa=bb, aaaaab=1〉
11〈a, b | aaa=bb, aaaaba=1〉
11〈a, b | aaa=bb, aaabaa=1〉
11〈a, b | aaab=1, aabbbbb=1〉
11〈a, b | aaab=1, ababbbb=1〉
11〈a, b | aaab=1, abbabbb=1〉
11〈a, b | aaab=1, abbbabb=1〉
11〈a, b | aaab=1, abbbbab=1〉
11〈a, b | aaab=1, abbbbba=1〉
11〈a, b | aaab=1, baabbbb=1〉
11〈a, b | aaab=1, bababbb=1〉
11〈a, b | aaab=1, babbabb=1〉
11〈a, b | aaab=1, babbbab=1〉
11〈a, b | aaab=1, babbbba=1〉
11〈a, b | aaab=1, bbaabbb=1〉
11〈a, b | aaab=1, bbababb=1〉
11〈a, b | aaab=1, bbabbab=1〉
11〈a, b | aaab=1, bbabbba=1〉
11〈a, b | aaab=1, bbbaabb=1〉
11〈a, b | aaab=1, bbbabab=1〉
11〈a, b | aaab=1, bbbabba=1〉
11〈a, b | aaab=1, bbbbaab=1〉
11〈a, b | aaab=1, bbbbaba=1〉
11〈a, b | aaab=1, bbbbbaa=1〉
11〈a, b | aaba=1, aabbbbb=1〉
11〈a, b | aaba=1, ababbbb=1〉
11〈a, b | aaba=1, abbabbb=1〉
11〈a, b | aaba=1, abbbabb=1〉
11〈a, b | aaba=1, abbbbab=1〉
11〈a, b | aaba=1, abbbbba=1〉
11〈a, b | aaba=1, baabbbb=1〉
11〈a, b | aaba=1, bababbb=1〉
11〈a, b | aaba=1, babbabb=1〉
11〈a, b | aaba=1, babbbab=1〉
11〈a, b | aaba=1, babbbba=1〉
11〈a, b | aaba=1, bbaabbb=1〉
11〈a, b | aaba=1, bbababb=1〉
11〈a, b | aaba=1, bbabbab=1〉
11〈a, b | aaba=1, bbabbba=1〉
11〈a, b | aaba=1, bbbaabb=1〉
11〈a, b | aaba=1, bbbabab=1〉
11〈a, b | aaba=1, bbbabba=1〉
11〈a, b | aaba=1, bbbbaab=1〉
11〈a, b | aaba=1, bbbbaba=1〉
11〈a, b | aaba=1, bbbbbaa=1〉
11〈a, b | aaab=1, abbbb=aa〉
11〈a, b | aaab=1, babbb=aa〉
11〈a, b | aaab=1, bbabb=aa〉
11〈a, b | aaab=1, bbbab=aa〉
11〈a, b | aaab=1, bbbba=aa〉
11〈a, b | aaab=1, bbbbb=ab〉
11〈a, b | aaab=1, bbbbb=ba〉
11〈a, b | aaba=1, abbbb=aa〉
11〈a, b | aaba=1, babbb=aa〉
11〈a, b | aaba=1, bbabb=aa〉
11〈a, b | aaba=1, bbbab=aa〉
11〈a, b | aaba=1, bbbba=aa〉
11〈a, b | aaba=1, bbbbb=ab〉
11〈a, b | aaba=1, bbbbb=ba〉
11〈a, b | aaa=b, aaaabbb=1〉
11〈a, b | aaa=b, aaababb=1〉
11〈a, b | aaa=b, aaabbab=1〉
11〈a, b | aaa=b, aaabbba=1〉
11〈a, b | aaa=b, aabaabb=1〉
11〈a, b | aaa=b, aababab=1〉
11〈a, b | aaa=b, aababba=1〉
11〈a, b | aaa=b, aabbaab=1〉
11〈a, b | aaa=b, aabbaba=1〉
11〈a, b | aaa=b, aabbbaa=1〉
11〈a, b | aaa=b, abaaabb=1〉
11〈a, b | aaa=b, abaabab=1〉
11〈a, b | aaa=b, abaabba=1〉
11〈a, b | aaa=b, ababaab=1〉
11〈a, b | aaa=b, abababa=1〉
11〈a, b | aaa=b, abbaaab=1〉
11〈a, b | aaa=b, baaaabb=1〉
11〈a, b | aaa=b, baaabab=1〉
11〈a, b | aaa=b, baabaab=1〉
11〈a, b | aab=1, abbbbbbb=1〉
11〈a, b | aab=1, babbbbbb=1〉
11〈a, b | aab=1, bbabbbbb=1〉
11〈a, b | aab=1, bbbabbbb=1〉
11〈a, b | aab=1, bbbbabbb=1〉
11〈a, b | aab=1, bbbbbabb=1〉
11〈a, b | aab=1, bbbbbbab=1〉
11〈a, b | aab=1, bbbbbbba=1〉
11〈a, b | aba=1, abbbbbbb=1〉
11〈a, b | aba=1, babbbbbb=1〉
11〈a, b | aba=1, bbabbbbb=1〉
11〈a, b | aba=1, bbbabbbb=1〉
11〈a, b | aab=1, bbbbb=aaa〉
11〈a, b | aba=1, bbbbb=aaa〉
11〈a, b | aa=b, aaabbbbb=1〉
11〈a, b | aa=b, aababbbb=1〉
11〈a, b | aa=b, aabbabbb=1〉
11〈a, b | aa=b, aabbbabb=1〉
11〈a, b | aa=b, aabbbbab=1〉
11〈a, b | aa=b, aabbbbba=1〉
11〈a, b | aa=b, abaabbbb=1〉
11〈a, b | aa=b, abababbb=1〉
11〈a, b | aa=b, ababbabb=1〉
11〈a, b | aa=b, ababbbab=1〉
11〈a, b | aa=b, ababbbba=1〉
11〈a, b | aa=b, abbaabbb=1〉
11〈a, b | aa=b, abbababb=1〉
11〈a, b | aa=b, abbabbab=1〉
11〈a, b | aa=b, abbabbba=1〉
11〈a, b | aa=b, abbbaabb=1〉
11〈a, b | aa=b, abbbabab=1〉
11〈a, b | aa=b, abbbbaab=1〉
11〈a, b | aa=b, baaabbbb=1〉
11〈a, b | aa=b, baababbb=1〉
11〈a, b | aa=b, baabbabb=1〉
11〈a, b | aa=b, baabbbab=1〉
11〈a, b | aa=b, babaabbb=1〉
11〈a, b | aa=b, babababb=1〉
11〈a, b | aa=b, bababbab=1〉
11〈a, b | aa=b, babbaabb=1〉
11〈a, b | aa=b, bbaaabbb=1〉
11〈a, b | aa=b, bbaababb=1〉