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〈a, b | aaa=bb, abbb=1〉

Monoid presentation of length 9

Properties

Completion parameters

Inverses of generators

Complete rewriting system

  1. a11 ⇒ 1
  2. b ⇒ a7

Cayley table

1aa2a3a4a5a6a7a8a9a10
11aa2a3a4a5a6a7a8a9a10
aaa2a3a4a5a6a7a8a9a101
a2a2a3a4a5a6a7a8a9a101a
a3a3a4a5a6a7a8a9a101aa2
a4a4a5a6a7a8a9a101aa2a3
a5a5a6a7a8a9a101aa2a3a4
a6a6a7a8a9a101aa2a3a4a5
a7a7a8a9a101aa2a3a4a5a6
a8a8a9a101aa2a3a4a5a6a7
a9a9a101aa2a3a4a5a6a7a8
a10a101aa2a3a4a5a6a7a8a9

Right Cayley graph

Others with same cardinality

40 unique, 221 total

Length:Presentation:Description:Related:
10 〈a, b | abb=aaa, bba=b〉 Finite non-commutative monoid with 11 elements
10 〈a, b | aaa=ab, baab=b〉 Finite non-commutative monoid with 11 elements 3 isomorphic
10 〈a, b | aaa=bb, abbb=a〉 Finite commutative monoid with 11 elements 4 isomorphic
10 〈a, b | aaa=bb, abbb=b〉 Finite commutative monoid with 11 elements 3 isomorphic
10 〈a, b | aab=aa, baaa=b〉 Finite non-commutative monoid with 11 elements 4 isomorphic
10 〈a, b | aaa=ab, abb=bb〉 Finite non-commutative monoid with 11 elements 3 isomorphic
10 〈a, b | aaa=ab, bbb=aa〉 Finite non-commutative monoid with 11 elements 2 isomorphic
10 〈a, b | aab=bb, bab=aa〉 Finite non-commutative monoid with 11 elements 2 isomorphic
10 〈a, b | aaa=b, aabbb=a〉 Finite commutative monoid with 11 elements 35 isomorphic
10 〈a, b | aaa=b, aabbb=b〉 Finite commutative monoid with 11 elements 11 isomorphic
10 〈a, b | aab=a, bbbbb=a〉 Finite commutative monoid with 11 elements 1 isomorphic
10 〈a, b | aba=b, abb=aaa〉 Finite non-commutative monoid with 11 elements
10 〈a, b | ab=aa, bbbb=aa〉 Finite non-commutative monoid with 11 elements 1 isomorphic
10 〈a, b | ab=aa, bbbb=ba〉 Finite non-commutative monoid with 11 elements
10 〈a, b | aa=b, abbbbb=b〉 Finite commutative monoid with 11 elements 32 isomorphic
10 〈a, b | ab=a, baaaaa=b〉 Finite non-commutative monoid with 11 elements 6 isomorphic
10 〈a, b | ab=a, bbaaa=bb〉 Finite non-commutative monoid with 11 elements 4 isomorphic
11 〈a, b | aaaa=ab, abbb=b〉 Finite commutative monoid with 11 elements 20 isomorphic
11 〈a, b | aaab=aa, baaa=b〉 Finite non-commutative monoid with 11 elements 2 isomorphic
11 〈a, b | aaab=bb, abbb=a〉 Finite commutative monoid with 11 elements 6 isomorphic
11 〈a, b | aaab=a, babbb=b〉 Finite non-commutative monoid with 11 elements 4 isomorphic
11 〈a, b | aaba=a, abbbb=b〉 Finite non-commutative monoid with 11 elements
11 〈a, b | aabb=a, baaab=b〉 Finite non-commutative monoid with 11 elements 7 isomorphic
11 〈a, b | abba=a, aaabb=b〉 Finite non-commutative monoid with 11 elements 2 isomorphic
11 〈a, b | aab=aa, bbbbb=a〉 Finite commutative monoid with 11 elements 1 isomorphic
11 〈a, b | aab=ab, bbbbb=a〉 Finite commutative monoid with 11 elements 8 isomorphic
11 〈a, b | aaa=bb, aaab=ab〉 Finite non-commutative monoid with 11 elements
11 〈a, b | aab=ab, aaaa=bb〉 Finite non-commutative monoid with 11 elements 1 isomorphic
11 〈a, b | aab=ba, aaaa=bb〉 Finite non-commutative monoid with 11 elements
11 〈a, b | aaa=a, aabbba=b〉 Finite non-commutative monoid with 11 elements
11 〈a, b | aab=a, baaaaa=b〉 Finite non-commutative monoid with 11 elements
11 〈a, b | aab=b, bbabbb=a〉 Finite commutative monoid with 11 elements 4 isomorphic
11 〈a, b | aba=a, aaaaab=b〉 Finite non-commutative monoid with 11 elements
11 〈a, b | aab=b, abba=aaa〉 Finite non-commutative monoid with 11 elements 1 isomorphic
11 〈a, b | aab=b, baaa=aaa〉 Finite non-commutative monoid with 11 elements
11 〈a, b | aab=b, bbbb=aaa〉 Finite commutative monoid with 11 elements
11 〈a, b | bb=aa, aaaaa=ab〉 Finite non-commutative monoid with 11 elements 7 isomorphic
11 〈a, b | bb=aa, aaaab=ab〉 Finite non-commutative monoid with 11 elements 7 isomorphic
11 〈a, b | ab=a, baaaa=bbb〉 Finite non-commutative monoid with 11 elements
11 〈a, b | ab=a, bbbaa=bbb〉 Finite non-commutative monoid with 11 elements

Other isomorphic instances

259 total

Length:Presentation:
9〈a, b | aaa=bb, babb=1〉
9〈a, b | aaab=1, abbbb=1〉
9〈a, b | aaab=1, babbb=1〉
9〈a, b | aaab=1, bbabb=1〉
9〈a, b | aaab=1, bbbab=1〉
9〈a, b | aaab=1, bbbba=1〉
9〈a, b | aaba=1, abbbb=1〉
9〈a, b | aaba=1, babbb=1〉
9〈a, b | aaba=1, bbabb=1〉
9〈a, b | aaba=1, bbbab=1〉
9〈a, b | aaba=1, bbbba=1〉
9〈a, b | aaa=b, aabbb=1〉
9〈a, b | aaa=b, ababb=1〉
9〈a, b | aaa=b, abbab=1〉
9〈a, b | aaa=b, abbba=1〉
9〈a, b | aaa=b, baabb=1〉
9〈a, b | aaa=b, babab=1〉
9〈a, b | aab=1, bbbbb=a〉
9〈a, b | aba=1, bbbbb=a〉
9〈a, b | aa=b, abbbbb=1〉
9〈a, b | aa=b, babbbb=1〉
9〈a, b | aa=b, bbabbb=1〉
10〈a, b | aaaa=b, aaabb=1〉
10〈a, b | aaaa=b, aabab=1〉
10〈a, b | aaaa=b, aabba=1〉
10〈a, b | aaaa=b, abaab=1〉
10〈a, b | aaaa=b, ababa=1〉
10〈a, b | aaaa=b, baaab=1〉
10〈a, b | aaa=bb, aaaab=1〉
10〈a, b | aaa=bb, aaaba=1〉
10〈a, b | aaa=bb, aabaa=1〉
10〈a, b | aab=1, abbbbbb=1〉
10〈a, b | aab=1, babbbbb=1〉
10〈a, b | aab=1, bbabbbb=1〉
10〈a, b | aab=1, bbbabbb=1〉
10〈a, b | aab=1, bbbbabb=1〉
10〈a, b | aab=1, bbbbbab=1〉
10〈a, b | aab=1, bbbbbba=1〉
10〈a, b | aba=1, abbbbbb=1〉
10〈a, b | aba=1, babbbbb=1〉
10〈a, b | aba=1, bbabbbb=1〉
10〈a, b | aba=1, bbbabbb=1〉
10〈a, b | aab=1, bbbb=aaa〉
10〈a, b | aba=1, bbbb=aaa〉
10〈a, b | aa=b, aaabbbb=1〉
10〈a, b | aa=b, aababbb=1〉
10〈a, b | aa=b, aabbabb=1〉
10〈a, b | aa=b, aabbbab=1〉
10〈a, b | aa=b, aabbbba=1〉
10〈a, b | aa=b, abaabbb=1〉
10〈a, b | aa=b, abababb=1〉
10〈a, b | aa=b, ababbab=1〉
10〈a, b | aa=b, ababbba=1〉
10〈a, b | aa=b, abbaabb=1〉
10〈a, b | aa=b, abbabab=1〉
10〈a, b | aa=b, abbabba=1〉
10〈a, b | aa=b, abbbaab=1〉
10〈a, b | aa=b, baaabbb=1〉
10〈a, b | aa=b, baababb=1〉
10〈a, b | aa=b, baabbab=1〉
10〈a, b | aa=b, babaabb=1〉
10〈a, b | aa=b, bababab=1〉
10〈a, b | aa=b, bbaaabb=1〉
11〈a, b | aaaa=abb, abbb=1〉
11〈a, b | aaaa=abb, babb=1〉
11〈a, b | aaaa=abb, bbab=1〉
11〈a, b | aaaa=abb, bbba=1〉
11〈a, b | aaaa=bab, abbb=1〉
11〈a, b | aaaa=bab, babb=1〉
11〈a, b | aaab=bbb, abbb=1〉
11〈a, b | aaab=bbb, babb=1〉
11〈a, b | aaab=bbb, bbab=1〉
11〈a, b | aaab=bbb, bbba=1〉
11〈a, b | aaba=bbb, abbb=1〉
11〈a, b | aaba=bbb, babb=1〉
11〈a, b | aaba=bbb, bbab=1〉
11〈a, b | aaba=bbb, bbba=1〉
11〈a, b | aaaab=a, abbbb=1〉
11〈a, b | aaaab=a, babbb=1〉
11〈a, b | aaaab=a, bbabb=1〉
11〈a, b | aaaab=a, bbbab=1〉
11〈a, b | aaaab=a, bbbba=1〉
11〈a, b | aaaba=a, abbbb=1〉
11〈a, b | aaaba=a, babbb=1〉
11〈a, b | aaaba=a, bbabb=1〉
11〈a, b | aaaba=a, bbbab=1〉
11〈a, b | aaaba=a, bbbba=1〉
11〈a, b | aaabb=b, abbbb=1〉
11〈a, b | aaabb=b, babbb=1〉
11〈a, b | aaabb=b, bbabb=1〉
11〈a, b | aaabb=b, bbbab=1〉
11〈a, b | aaabb=b, bbbba=1〉
11〈a, b | aabaa=a, abbbb=1〉
11〈a, b | aabaa=a, babbb=1〉
11〈a, b | aabaa=a, bbabb=1〉
11〈a, b | aabab=b, abbbb=1〉
11〈a, b | aabab=b, babbb=1〉
11〈a, b | aabab=b, bbabb=1〉
11〈a, b | aabab=b, bbbab=1〉
11〈a, b | aabab=b, bbbba=1〉
11〈a, b | aabba=b, abbbb=1〉
11〈a, b | aabba=b, babbb=1〉
11〈a, b | aabba=b, bbabb=1〉
11〈a, b | aabba=b, bbbab=1〉
11〈a, b | aabba=b, bbbba=1〉
11〈a, b | abaab=b, abbbb=1〉
11〈a, b | abaab=b, babbb=1〉
11〈a, b | abaab=b, bbabb=1〉
11〈a, b | abaab=b, bbbab=1〉
11〈a, b | abaab=b, bbbba=1〉
11〈a, b | ababa=b, abbbb=1〉
11〈a, b | ababa=b, babbb=1〉
11〈a, b | ababa=b, bbabb=1〉
11〈a, b | abbba=a, baaaa=1〉
11〈a, b | baaab=b, babbb=1〉
11〈a, b | baaab=b, bbabb=1〉
11〈a, b | aaaa=ab, aabbb=1〉
11〈a, b | aaaa=ab, ababb=1〉
11〈a, b | aaaa=ab, abbab=1〉
11〈a, b | aaaa=ab, abbba=1〉
11〈a, b | aaaa=ab, baabb=1〉
11〈a, b | aaaa=ab, babab=1〉
11〈a, b | aaaa=ab, babba=1〉
11〈a, b | aaaa=ab, bbaab=1〉
11〈a, b | aaaa=ab, bbaba=1〉
11〈a, b | aaaa=ab, bbbaa=1〉
11〈a, b | aaab=bb, aabbb=1〉
11〈a, b | aaab=bb, ababb=1〉
11〈a, b | aaab=bb, abbab=1〉
11〈a, b | aaab=bb, abbba=1〉
11〈a, b | aaab=bb, baabb=1〉
11〈a, b | aaab=bb, babab=1〉
11〈a, b | aaab=bb, babba=1〉
11〈a, b | aaab=bb, bbaab=1〉
11〈a, b | aaab=bb, bbaba=1〉
11〈a, b | aaab=bb, bbbaa=1〉
11〈a, b | aaba=bb, aabbb=1〉
11〈a, b | aaba=bb, ababb=1〉
11〈a, b | aaba=bb, abbab=1〉
11〈a, b | aaba=bb, abbba=1〉
11〈a, b | aaba=bb, baabb=1〉
11〈a, b | aaba=bb, babab=1〉
11〈a, b | aaba=bb, babba=1〉
11〈a, b | aaba=bb, bbaab=1〉
11〈a, b | aaba=bb, bbaba=1〉
11〈a, b | aaba=bb, bbbaa=1〉
11〈a, b | aaa=ab, abbbbb=1〉
11〈a, b | aaa=ab, babbbb=1〉
11〈a, b | aaa=ab, bbabbb=1〉
11〈a, b | aaa=ab, bbbabb=1〉
11〈a, b | aaa=ab, bbbbab=1〉
11〈a, b | aaa=ab, bbbbba=1〉
11〈a, b | aab=bb, abbbbb=1〉
11〈a, b | aab=bb, babbbb=1〉
11〈a, b | aab=bb, bbabbb=1〉
11〈a, b | aab=bb, bbbabb=1〉
11〈a, b | aab=bb, bbbbab=1〉
11〈a, b | aab=bb, bbbbba=1〉
11〈a, b | aba=bb, abbbbb=1〉
11〈a, b | aba=bb, babbbb=1〉
11〈a, b | aba=bb, bbabbb=1〉
11〈a, b | aaab=1, aabbbb=a〉
11〈a, b | aaab=1, ababbb=a〉
11〈a, b | aaab=1, abbabb=a〉
11〈a, b | aaab=1, abbbab=a〉
11〈a, b | aaab=1, abbbba=a〉
11〈a, b | aaab=1, abbbbb=b〉
11〈a, b | aaab=1, baabbb=a〉
11〈a, b | aaab=1, bababb=a〉
11〈a, b | aaab=1, babbab=a〉
11〈a, b | aaab=1, babbba=a〉
11〈a, b | aaab=1, babbbb=b〉
11〈a, b | aaab=1, bbaabb=a〉
11〈a, b | aaab=1, bbabab=a〉
11〈a, b | aaab=1, bbabba=a〉
11〈a, b | aaab=1, bbabbb=b〉
11〈a, b | aaab=1, bbbaab=a〉
11〈a, b | aaab=1, bbbaba=a〉
11〈a, b | aaab=1, bbbabb=b〉
11〈a, b | aaab=1, bbbbaa=a〉
11〈a, b | aaab=1, bbbbab=b〉
11〈a, b | aaab=1, bbbbba=b〉
11〈a, b | aaba=1, aabbbb=a〉
11〈a, b | aaba=1, ababbb=a〉
11〈a, b | aaba=1, abbabb=a〉
11〈a, b | aaba=1, abbbab=a〉
11〈a, b | aaba=1, abbbba=a〉
11〈a, b | aaba=1, abbbbb=b〉
11〈a, b | aaba=1, baabbb=a〉
11〈a, b | aaba=1, bababb=a〉
11〈a, b | aaba=1, babbab=a〉
11〈a, b | aaba=1, babbba=a〉
11〈a, b | aaba=1, babbbb=b〉
11〈a, b | aaba=1, bbaabb=a〉
11〈a, b | aaba=1, bbabab=a〉
11〈a, b | aaba=1, bbabba=a〉
11〈a, b | aaba=1, bbabbb=b〉
11〈a, b | aaba=1, bbbaab=a〉
11〈a, b | aaba=1, bbbaba=a〉
11〈a, b | aaba=1, bbbabb=b〉
11〈a, b | aaba=1, bbbbaa=a〉
11〈a, b | aaba=1, bbbbab=b〉
11〈a, b | aaba=1, bbbbba=b〉
11〈a, b | aaab=1, aaaaa=bb〉
11〈a, b | aaba=1, aaaaa=bb〉
11〈a, b | aaa=b, aaaaabb=1〉
11〈a, b | aaa=b, aaaabab=1〉
11〈a, b | aaa=b, aaaabba=1〉
11〈a, b | aaa=b, aaabaab=1〉
11〈a, b | aaa=b, aaababa=1〉
11〈a, b | aaa=b, aaabbaa=1〉
11〈a, b | aaa=b, aabaaab=1〉
11〈a, b | aaa=b, aabaaba=1〉
11〈a, b | aaa=b, aababaa=1〉
11〈a, b | aaa=b, abaaaab=1〉
11〈a, b | aaa=b, abaaaba=1〉
11〈a, b | aaa=b, baaaaab=1〉
11〈a, b | aab=1, abbbbb=aa〉
11〈a, b | aab=1, babbbb=aa〉
11〈a, b | aab=1, bbabbb=aa〉
11〈a, b | aab=1, bbbabb=aa〉
11〈a, b | aab=1, bbbbab=aa〉
11〈a, b | aab=1, bbbbba=aa〉
11〈a, b | aab=1, bbbbbb=ab〉
11〈a, b | aab=1, bbbbbb=ba〉
11〈a, b | aba=1, abbbbb=aa〉
11〈a, b | aba=1, babbbb=aa〉
11〈a, b | aba=1, bbabbb=aa〉
11〈a, b | aba=1, bbbbbb=ab〉
11〈a, b | aab=1, aaaaa=bbb〉
11〈a, b | aba=1, aaaaa=bbb〉
11〈a, b | aa=b, aaaaabbb=1〉
11〈a, b | aa=b, aaaababb=1〉
11〈a, b | aa=b, aaaabbab=1〉
11〈a, b | aa=b, aaaabbba=1〉
11〈a, b | aa=b, aaabaabb=1〉
11〈a, b | aa=b, aaababab=1〉
11〈a, b | aa=b, aaababba=1〉
11〈a, b | aa=b, aaabbaab=1〉
11〈a, b | aa=b, aaabbaba=1〉
11〈a, b | aa=b, aaabbbaa=1〉
11〈a, b | aa=b, aabaaabb=1〉
11〈a, b | aa=b, aabaabab=1〉
11〈a, b | aa=b, aabaabba=1〉
11〈a, b | aa=b, aababaab=1〉
11〈a, b | aa=b, aabababa=1〉
11〈a, b | aa=b, aababbaa=1〉
11〈a, b | aa=b, aabbaaab=1〉
11〈a, b | aa=b, aabbaaba=1〉
11〈a, b | aa=b, abaaaabb=1〉
11〈a, b | aa=b, abaaabab=1〉
11〈a, b | aa=b, abaaabba=1〉
11〈a, b | aa=b, abaabaab=1〉
11〈a, b | aa=b, abaababa=1〉
11〈a, b | aa=b, ababaaab=1〉
11〈a, b | aa=b, abbaaaab=1〉
11〈a, b | aa=b, baaaaabb=1〉
11〈a, b | aa=b, baaaabab=1〉
11〈a, b | aa=b, baaabaab=1〉