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〈a, b | aaaa=1, abbb=1〉

Monoid presentation of length 8

Properties

Completion parameters

Inverses of generators

Complete rewriting system

  1. b12 ⇒ 1
  2. a ⇒ b9

Cayley table

1bb2b3b4b5b6b7b8b9b10b11
11bb2b3b4b5b6b7b8b9b10b11
bbb2b3b4b5b6b7b8b9b10b111
b2b2b3b4b5b6b7b8b9b10b111b
b3b3b4b5b6b7b8b9b10b111bb2
b4b4b5b6b7b8b9b10b111bb2b3
b5b5b6b7b8b9b10b111bb2b3b4
b6b6b7b8b9b10b111bb2b3b4b5
b7b7b8b9b10b111bb2b3b4b5b6
b8b8b9b10b111bb2b3b4b5b6b7
b9b9b10b111bb2b3b4b5b6b7b8
b10b10b111bb2b3b4b5b6b7b8b9
b11b111bb2b3b4b5b6b7b8b9b10

Right Cayley graph

Others with same cardinality

51 unique, 334 total

Length:Presentation:Description:Related:
7 〈a, b | aab=a, bbb=1〉 Finite non-commutative monoid with 12 elements 8 isomorphic, 12 anti-isomorphic
7 〈a, b | ab=aa, bbb=1〉 Finite non-commutative monoid with 12 elements 9 isomorphic
8 〈a, b | aba=ab, bbb=1〉 Finite non-commutative monoid with 12 elements
8 〈a, b | ab=aa, bbb=b〉 Finite non-commutative monoid with 12 elements
8 〈a, b | aaa=1, aabb=b〉 Finite non-commutative monoid with 12 elements 16 isomorphic
9 〈a, b | aab=bb, aba=a〉 Finite non-commutative monoid with 12 elements 2 isomorphic
9 〈a, b | aba=b, aaabb=1〉 Finite non-Abelian group with 12 elements 19 isomorphic
9 〈a, b | aaa=a, bbbb=a〉 Finite commutative monoid with 12 elements 6 isomorphic
9 〈a, b | aaa=b, bbbb=a〉 Finite commutative monoid with 12 elements 27 isomorphic
9 〈a, b | aaa=b, bbbb=b〉 Finite commutative monoid with 12 elements 23 isomorphic
9 〈a, b | ab=aa, bbb=bb〉 Finite non-commutative monoid with 12 elements
9 〈a, b | aaa=1, aabab=b〉 Finite non-commutative monoid with 12 elements 8 isomorphic, 4 anti-isomorphic
10 〈a, b | bab=aba, aabb=1〉 Finite non-Abelian group with 12 elements 4 isomorphic
10 〈a, b | aaa=aa, bbbb=a〉 Finite commutative monoid with 12 elements
10 〈a, b | aaa=ab, bbbb=a〉 Finite commutative monoid with 12 elements 7 isomorphic
10 〈a, b | aaa=bb, bbbb=a〉 Finite commutative monoid with 12 elements 43 isomorphic
10 〈a, b | aab=bb, abba=a〉 Finite non-commutative monoid with 12 elements 6 isomorphic
10 〈a, b | aaa=ab, bab=bb〉 Finite non-commutative monoid with 12 elements 1 isomorphic
10 〈a, b | aaa=a, aaab=bb〉 Finite non-commutative monoid with 12 elements
10 〈a, b | aaa=b, bbbb=bb〉 Finite commutative monoid with 12 elements 4 isomorphic
10 〈a, b | aab=a, bbbb=ba〉 Finite non-commutative monoid with 12 elements
10 〈a, b | aab=a, bbbb=bb〉 Finite non-commutative monoid with 12 elements
10 〈a, b | aba=a, bbbb=ab〉 Finite non-commutative monoid with 12 elements
10 〈a, b | ab=aa, bbaa=bb〉 Finite non-commutative monoid with 12 elements 2 isomorphic
11 〈a, b | aaaa=aa, abab=b〉 Finite non-commutative monoid with 12 elements
11 〈a, b | aaab=bb, aaba=a〉 Finite non-commutative monoid with 12 elements 2 isomorphic
11 〈a, b | aab=aaa, baaa=b〉 Finite non-commutative monoid with 12 elements 4 isomorphic
11 〈a, b | aab=aaa, bbbb=a〉 Finite commutative monoid with 12 elements 2 isomorphic
11 〈a, b | aab=ba, ababbb=1〉 Finite non-Abelian group with 12 elements 5 isomorphic
11 〈a, b | aaa=aa, abbbb=b〉 Finite non-commutative monoid with 12 elements
11 〈a, b | aaa=ab, aabb=bb〉 Finite non-commutative monoid with 12 elements 2 isomorphic
11 〈a, b | aaa=bb, aabb=ab〉 Finite non-commutative monoid with 12 elements 2 isomorphic
11 〈a, b | aaa=bb, aabb=ba〉 Finite non-commutative monoid with 12 elements 1 isomorphic
11 〈a, b | aab=aa, abab=bb〉 Finite non-commutative monoid with 12 elements
11 〈a, b | aab=bb, aaaa=ab〉 Finite non-commutative monoid with 12 elements 1 isomorphic
11 〈a, b | aab=bb, aaaa=ba〉 Finite non-commutative monoid with 12 elements
11 〈a, b | aba=bb, aabb=aa〉 Finite non-commutative monoid with 12 elements 2 isomorphic
11 〈a, b | aab=a, baaaa=bb〉 Finite non-commutative monoid with 12 elements
11 〈a, b | aba=b, bbbbb=aa〉 Finite commutative monoid with 12 elements
11 〈a, b | aaa=b, bbbb=abb〉 Finite commutative monoid with 12 elements 2 isomorphic
11 〈a, b | aab=a, bbaa=bbb〉 Finite non-commutative monoid with 12 elements
11 〈a, b | aab=b, aaaa=bba〉 Finite non-commutative monoid with 12 elements
11 〈a, b | ab=aa, baaaaa=b〉 Finite non-commutative monoid with 12 elements 30 isomorphic
11 〈a, b | bb=aa, aaaaab=a〉 Finite commutative monoid with 12 elements 15 isomorphic
11 〈a, b | ab=aa, baaaa=bb〉 Finite non-commutative monoid with 12 elements 7 isomorphic
11 〈a, b | bb=aa, aaaa=aba〉 Finite non-commutative monoid with 12 elements 4 isomorphic
11 〈a, b | bb=aa, aaab=aba〉 Finite non-commutative monoid with 12 elements 3 isomorphic
11 〈a, b | bb=aa, abab=aba〉 Finite non-commutative monoid with 12 elements
11 〈a, b | aa=a, abbbbbb=b〉 Finite non-commutative monoid with 12 elements
11 〈a, b | ab=a, baaaaa=bb〉 Finite non-commutative monoid with 12 elements
11 〈a, b | ab=a, bbaaa=bbb〉 Finite non-commutative monoid with 12 elements

Other isomorphic instances

325 total

Length:Presentation:
8〈a, b | aaaa=1, babb=1〉
8〈a, b | aaa=b, bbbb=1〉
8〈a, b | aaa=1, abbbb=1〉
8〈a, b | aaa=1, babbb=1〉
8〈a, b | aaa=1, bbabb=1〉
8〈a, b | aaa=1, bbbb=a〉
9〈a, b | aaaa=1, ababb=1〉
9〈a, b | aaaa=1, abbab=1〉
9〈a, b | aaaa=1, babab=1〉
9〈a, b | aaa=1, aabbbb=1〉
9〈a, b | aaa=1, abbbba=1〉
9〈a, b | aaa=1, baabbb=1〉
9〈a, b | aaa=1, bbaabb=1〉
9〈a, b | aab=1, bbbbbb=1〉
9〈a, b | aba=1, bbbbbb=1〉
9〈a, b | aaa=1, bbbb=aa〉
9〈a, b | aa=b, bbbbbb=1〉
9〈a, b | aa=1, abbbbbb=1〉
9〈a, b | aa=1, babbbbb=1〉
9〈a, b | aa=1, bbabbbb=1〉
9〈a, b | aa=1, bbbabbb=1〉
9〈a, b | aa=1, bbbbbb=a〉
10〈a, b | aaab=bb, bbbb=1〉
10〈a, b | bbb=aaa, aaaa=1〉
10〈a, b | bbb=aaa, aaab=1〉
10〈a, b | bbb=aaa, aaba=1〉
10〈a, b | bbb=aaa, aabb=1〉
10〈a, b | bbb=aaa, abba=1〉
10〈a, b | aaaa=a, abbbb=1〉
10〈a, b | aaaa=a, babbb=1〉
10〈a, b | aaaa=a, bbabb=1〉
10〈a, b | aaab=b, abbbb=1〉
10〈a, b | aaab=b, babbb=1〉
10〈a, b | aaab=b, bbabb=1〉
10〈a, b | aaab=b, bbbab=1〉
10〈a, b | aaab=b, bbbba=1〉
10〈a, b | aaba=b, abbbb=1〉
10〈a, b | aaba=b, babbb=1〉
10〈a, b | aaba=b, bbabb=1〉
10〈a, b | aaba=b, bbbab=1〉
10〈a, b | aaba=b, bbbba=1〉
10〈a, b | aaa=bb, aabab=1〉
10〈a, b | aaa=bb, abaab=1〉
10〈a, b | aaa=bb, ababa=1〉
10〈a, b | aaaa=1, aaabbb=1〉
10〈a, b | aaaa=1, aabbba=1〉
10〈a, b | aaaa=1, baaabb=1〉
10〈a, b | aaaa=1, aabbb=a〉
10〈a, b | aaaa=1, ababb=a〉
10〈a, b | aaaa=1, abbab=a〉
10〈a, b | aaaa=1, abbba=a〉
10〈a, b | aaab=1, abbbb=a〉
10〈a, b | aaab=1, babbb=a〉
10〈a, b | aaab=1, bbabb=a〉
10〈a, b | aaab=1, bbbab=a〉
10〈a, b | aaab=1, bbbba=a〉
10〈a, b | aaab=1, bbbbb=b〉
10〈a, b | aaba=1, abbbb=a〉
10〈a, b | aaba=1, babbb=a〉
10〈a, b | aaba=1, bbabb=a〉
10〈a, b | aaba=1, bbbab=a〉
10〈a, b | aaba=1, bbbba=a〉
10〈a, b | aaba=1, bbbbb=b〉
10〈a, b | aabb=1, aaaaa=b〉
10〈a, b | abab=1, aaaaa=b〉
10〈a, b | abba=1, aaaaa=b〉
10〈a, b | abba=1, bbbbb=a〉
10〈a, b | aaa=b, aaabbb=1〉
10〈a, b | aaa=b, aababb=1〉
10〈a, b | aaa=b, aabbab=1〉
10〈a, b | aaa=b, aabbba=1〉
10〈a, b | aaa=b, abaabb=1〉
10〈a, b | aaa=b, ababab=1〉
10〈a, b | aaa=b, ababba=1〉
10〈a, b | aaa=b, abbaab=1〉
10〈a, b | aaa=b, baaabb=1〉
10〈a, b | aaa=b, baabab=1〉
10〈a, b | bb=aa, aaaaab=1〉
10〈a, b | bb=aa, aaaaba=1〉
10〈a, b | bb=aa, aaabaa=1〉
10〈a, b | bb=aa, aaabbb=1〉
10〈a, b | bb=aa, aababb=1〉
10〈a, b | bb=aa, aabbab=1〉
10〈a, b | bb=aa, aabbba=1〉
10〈a, b | bb=aa, ababba=1〉
10〈a, b | bb=aa, abbaab=1〉
10〈a, b | aaa=1, abababb=1〉
10〈a, b | aaa=1, ababbab=1〉
10〈a, b | aaa=1, abbabab=1〉
10〈a, b | aaa=1, bababab=1〉
10〈a, b | aaa=1, aabbbb=a〉
10〈a, b | aaa=1, ababbb=a〉
10〈a, b | aaa=1, abbabb=a〉
10〈a, b | aaa=1, abbbab=a〉
10〈a, b | aaa=1, abbbba=a〉
10〈a, b | aaa=1, abbbb=aa〉
10〈a, b | aab=1, bbbbb=aa〉
10〈a, b | aba=1, bbbbb=aa〉
10〈a, b | aa=b, aabbbbb=1〉
10〈a, b | aa=b, ababbbb=1〉
10〈a, b | aa=b, abbabbb=1〉
10〈a, b | aa=b, abbbabb=1〉
10〈a, b | aa=b, abbbbab=1〉
10〈a, b | aa=b, abbbbba=1〉
10〈a, b | aa=b, baabbbb=1〉
10〈a, b | aa=b, bababbb=1〉
10〈a, b | aa=b, babbabb=1〉
10〈a, b | aa=b, babbbab=1〉
10〈a, b | aa=b, bbaabbb=1〉
10〈a, b | aa=b, bbababb=1〉
11〈a, b | aaba=bbb, bbbb=1〉
11〈a, b | aaaaa=a, ababb=1〉
11〈a, b | aaaaa=a, abbab=1〉
11〈a, b | aaaaa=a, babab=1〉
11〈a, b | aaaab=b, ababb=1〉
11〈a, b | aaaab=b, abbab=1〉
11〈a, b | aaaab=b, babab=1〉
11〈a, b | aaaab=b, babba=1〉
11〈a, b | aaaab=b, bbaba=1〉
11〈a, b | aaaba=b, aabbb=1〉
11〈a, b | aaaba=b, ababb=1〉
11〈a, b | aaaba=b, abbab=1〉
11〈a, b | aaaba=b, abbba=1〉
11〈a, b | aaaba=b, baabb=1〉
11〈a, b | aaaba=b, babab=1〉
11〈a, b | aaaba=b, babba=1〉
11〈a, b | aaaba=b, bbaab=1〉
11〈a, b | aaaba=b, bbaba=1〉
11〈a, b | aaaba=b, bbbaa=1〉
11〈a, b | aabaa=b, ababb=1〉
11〈a, b | aabaa=b, abbab=1〉
11〈a, b | aabaa=b, babab=1〉
11〈a, b | aaaa=bb, aaaab=1〉
11〈a, b | aaaa=bb, aaaba=1〉
11〈a, b | aaaa=bb, aabaa=1〉
11〈a, b | aabab=1, aaaaaa=1〉
11〈a, b | abaab=1, aaaaaa=1〉
11〈a, b | ababa=1, aaaaaa=1〉
11〈a, b | aaaa=a, aabbbb=1〉
11〈a, b | aaaa=a, abbbba=1〉
11〈a, b | aaaa=a, baabbb=1〉
11〈a, b | aaaa=a, bbaabb=1〉
11〈a, b | aaaa=b, aaaabb=1〉
11〈a, b | aaaa=b, aaabab=1〉
11〈a, b | aaaa=b, aaabba=1〉
11〈a, b | aaaa=b, aabaab=1〉
11〈a, b | aaaa=b, aababa=1〉
11〈a, b | aaaa=b, aabbaa=1〉
11〈a, b | aaaa=b, abaaab=1〉
11〈a, b | aaaa=b, abaaba=1〉
11〈a, b | aaaa=b, baaaab=1〉
11〈a, b | aaab=b, aabbbb=1〉
11〈a, b | aaab=b, abbbba=1〉
11〈a, b | aaab=b, baabbb=1〉
11〈a, b | aaab=b, bbaabb=1〉
11〈a, b | aaab=b, bbbaab=1〉
11〈a, b | aaab=b, bbbbaa=1〉
11〈a, b | aaba=b, aabbbb=1〉
11〈a, b | aaba=b, ababbb=1〉
11〈a, b | aaba=b, abbbab=1〉
11〈a, b | aaba=b, abbbba=1〉
11〈a, b | aaba=b, baabbb=1〉
11〈a, b | aaba=b, bababb=1〉
11〈a, b | aaba=b, babbba=1〉
11〈a, b | aaba=b, bbaabb=1〉
11〈a, b | aaba=b, bbabab=1〉
11〈a, b | aaba=b, bbbaab=1〉
11〈a, b | aaba=b, bbbaba=1〉
11〈a, b | aaba=b, bbbbaa=1〉
11〈a, b | aabb=a, aaaaaa=1〉
11〈a, b | abab=a, aaaaaa=1〉
11〈a, b | abba=a, aaaaaa=1〉
11〈a, b | aab=bb, bbbbbb=1〉
11〈a, b | aaaa=1, aababab=1〉
11〈a, b | aaaa=1, abaabab=1〉
11〈a, b | aaaa=1, ababaab=1〉
11〈a, b | aaaa=1, abababa=1〉
11〈a, b | aaaa=1, aababb=a〉
11〈a, b | aaaa=1, aabbab=a〉
11〈a, b | aaaa=1, ababab=a〉
11〈a, b | aaaa=1, ababba=a〉
11〈a, b | aaaa=1, baaabb=a〉
11〈a, b | aaaa=1, babab=aa〉
11〈a, b | aaa=a, abbbbbb=1〉
11〈a, b | aaa=a, babbbbb=1〉
11〈a, b | aaa=a, bbabbbb=1〉
11〈a, b | aaa=a, bbbabbb=1〉
11〈a, b | aab=b, abbbbbb=1〉
11〈a, b | aab=b, babbbbb=1〉
11〈a, b | aab=b, bbabbbb=1〉
11〈a, b | aab=b, bbbabbb=1〉
11〈a, b | aab=b, bbbbabb=1〉
11〈a, b | aab=b, bbbbbab=1〉
11〈a, b | aab=b, bbbbbba=1〉
11〈a, b | aba=b, abbbbbb=1〉
11〈a, b | aba=b, babbbbb=1〉
11〈a, b | aba=b, bbabbbb=1〉
11〈a, b | aba=b, bbbabbb=1〉
11〈a, b | aaa=1, aaaabbbb=1〉
11〈a, b | aaa=1, aaababbb=1〉
11〈a, b | aaa=1, aaabbabb=1〉
11〈a, b | aaa=1, aaabbbab=1〉
11〈a, b | aaa=1, aaabbbba=1〉
11〈a, b | aaa=1, aababbba=1〉
11〈a, b | aaa=1, aabbabba=1〉
11〈a, b | aaa=1, aabbbaba=1〉
11〈a, b | aaa=1, aabbbbaa=1〉
11〈a, b | aaa=1, abaaabbb=1〉
11〈a, b | aaa=1, abbaaabb=1〉
11〈a, b | aaa=1, abbbaaab=1〉
11〈a, b | aaa=1, baaaabbb=1〉
11〈a, b | aaa=1, baaababb=1〉
11〈a, b | aaa=1, baaabbab=1〉
11〈a, b | aaa=1, babaaabb=1〉
11〈a, b | aaa=1, bbaaaabb=1〉
11〈a, b | aaa=1, aaabbbb=a〉
11〈a, b | aaa=1, aabbbba=a〉
11〈a, b | aaa=1, abaabbb=a〉
11〈a, b | aaa=1, abbaabb=a〉
11〈a, b | aaa=1, abbbaab=a〉
11〈a, b | aaa=1, baaabbb=a〉
11〈a, b | aaa=1, bababab=a〉
11〈a, b | aaa=1, bbaaabb=a〉
11〈a, b | aab=1, abbbbbb=a〉
11〈a, b | aab=1, babbbbb=a〉
11〈a, b | aab=1, bbabbbb=a〉
11〈a, b | aab=1, bbbabbb=a〉
11〈a, b | aab=1, bbbbabb=a〉
11〈a, b | aab=1, bbbbbab=a〉
11〈a, b | aab=1, bbbbbba=a〉
11〈a, b | aab=1, bbbbbbb=b〉
11〈a, b | aba=1, abbbbbb=a〉
11〈a, b | aba=1, babbbbb=a〉
11〈a, b | aba=1, bbabbbb=a〉
11〈a, b | aba=1, bbbabbb=a〉
11〈a, b | aba=1, bbbbbbb=b〉
11〈a, b | aaa=1, bababb=aa〉
11〈a, b | aaa=1, babbab=aa〉
11〈a, b | aaa=1, abbbb=aaa〉
11〈a, b | aaa=1, babbb=aaa〉
11〈a, b | aaa=1, bbabb=aaa〉
11〈a, b | aaa=1, bbbb=aaaa〉
11〈a, b | aab=1, bbbb=aaaa〉
11〈a, b | aba=1, bbbb=aaaa〉
11〈a, b | aa=b, aaaabbbb=1〉
11〈a, b | aa=b, aaababbb=1〉
11〈a, b | aa=b, aaabbabb=1〉
11〈a, b | aa=b, aaabbbab=1〉
11〈a, b | aa=b, aaabbbba=1〉
11〈a, b | aa=b, aabaabbb=1〉
11〈a, b | aa=b, aabababb=1〉
11〈a, b | aa=b, aababbab=1〉
11〈a, b | aa=b, aababbba=1〉
11〈a, b | aa=b, aabbaabb=1〉
11〈a, b | aa=b, aabbabab=1〉
11〈a, b | aa=b, aabbabba=1〉
11〈a, b | aa=b, aabbbaab=1〉
11〈a, b | aa=b, aabbbaba=1〉
11〈a, b | aa=b, aabbbbaa=1〉
11〈a, b | aa=b, abaaabbb=1〉
11〈a, b | aa=b, abaababb=1〉
11〈a, b | aa=b, abaabbab=1〉
11〈a, b | aa=b, abaabbba=1〉
11〈a, b | aa=b, ababaabb=1〉
11〈a, b | aa=b, abababab=1〉
11〈a, b | aa=b, abababba=1〉
11〈a, b | aa=b, ababbaab=1〉
11〈a, b | aa=b, ababbaba=1〉
11〈a, b | aa=b, abbaaabb=1〉
11〈a, b | aa=b, abbaabab=1〉
11〈a, b | aa=b, abbaabba=1〉
11〈a, b | aa=b, abbabaab=1〉
11〈a, b | aa=b, abbbaaab=1〉
11〈a, b | aa=b, baaaabbb=1〉
11〈a, b | aa=b, baaababb=1〉
11〈a, b | aa=b, baaabbab=1〉
11〈a, b | aa=b, baabaabb=1〉
11〈a, b | aa=b, baababab=1〉
11〈a, b | aa=b, baabbaab=1〉
11〈a, b | aa=b, babaaabb=1〉
11〈a, b | aa=b, babaabab=1〉
11〈a, b | aa=b, bbaaaabb=1〉
11〈a, b | aa=1, aaabbbbbb=1〉
11〈a, b | aa=1, aababbbbb=1〉
11〈a, b | aa=1, aabbabbbb=1〉
11〈a, b | aa=1, aabbbabbb=1〉
11〈a, b | aa=1, aabbbbabb=1〉
11〈a, b | aa=1, aabbbbbab=1〉
11〈a, b | aa=1, aabbbbbba=1〉
11〈a, b | aa=1, abaabbbbb=1〉
11〈a, b | aa=1, ababbbbba=1〉
11〈a, b | aa=1, abbaabbbb=1〉
11〈a, b | aa=1, abbabbbba=1〉
11〈a, b | aa=1, abbbaabbb=1〉
11〈a, b | aa=1, abbbabbba=1〉
11〈a, b | aa=1, abbbbaabb=1〉
11〈a, b | aa=1, abbbbbaab=1〉
11〈a, b | aa=1, baaabbbbb=1〉
11〈a, b | aa=1, baababbbb=1〉
11〈a, b | aa=1, baabbabbb=1〉
11〈a, b | aa=1, baabbbabb=1〉
11〈a, b | aa=1, baabbbbab=1〉
11〈a, b | aa=1, babaabbbb=1〉
11〈a, b | aa=1, babbaabbb=1〉
11〈a, b | aa=1, babbbaabb=1〉
11〈a, b | aa=1, bbaaabbbb=1〉
11〈a, b | aa=1, bbaababbb=1〉
11〈a, b | aa=1, bbaabbabb=1〉
11〈a, b | aa=1, bbabaabbb=1〉
11〈a, b | aa=1, bbbaaabbb=1〉
11〈a, b | aa=1, aabbbbbb=a〉
11〈a, b | aa=1, ababbbbb=a〉
11〈a, b | aa=1, abbabbbb=a〉
11〈a, b | aa=1, abbbabbb=a〉
11〈a, b | aa=1, abbbbabb=a〉
11〈a, b | aa=1, abbbbbab=a〉
11〈a, b | aa=1, abbbbbba=a〉
11〈a, b | aa=1, baabbbbb=a〉
11〈a, b | aa=1, bbaabbbb=a〉
11〈a, b | aa=1, bbbaabbb=a〉
11〈a, b | aa=1, abbbbbb=aa〉
11〈a, b | aa=1, babbbbb=aa〉
11〈a, b | aa=1, bbabbbb=aa〉
11〈a, b | aa=1, bbbabbb=aa〉
11〈a, b | aa=1, bbbbbb=aaa〉