#1427 ⟨a, b | abba=b, baba=1⟩

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Properties

Element profile

Complete rewriting system

Format:
Word to reduce:
Tips:
  • Lowercase letters stand for generators.
  • Spaces are ignored.
  • Numbers repeat the previous letter, e.g. b90.
Reduction strategy:
Path to normal form: 1 
1
  1. b3 ⇒ 1
  2. ba ⇒ ab2
  3. a2 ⇒ 1 
# ab:abba=b,baba=1 b/a
bbb=1
ba=abb
aa=1

Cayley table

1ababb2ab2
11ababb2ab2
aa1abbab2b2
bbab2b2a1ab
ababb2ab21ab
b2b2ab1ab2ba
ab2ab2bab2ab1

Right Cayley graph

Left Cayley graph

Others with same cardinality

19 unique, 1859 total

Σ#PresentationDescriptionRelated
622⟨a, b | ab=aa, bb=1⟩Finite non-commutative monoid with 6 elements44 iso, 63 anti-iso
626⟨a, b | aaa=1, abb=1⟩Isomorphic to ℤ61373 iso
7160⟨a, b | ab=aa, bb=b⟩Finite non-commutative monoid with 6 elements4 anti-iso
7245⟨a, b | aa=a, bbb=a⟩Isomorphic to ℕ(6 = 3)49 iso
7257⟨a, b | aa=b, bbb=a⟩Isomorphic to ℕ(6 = 1)61 iso
7258⟨a, b | aa=b, bbb=b⟩Isomorphic to ℕ(6 = 2)55 iso
8639⟨a, b | ab=aa, baa=b⟩Finite non-commutative monoid with 6 elements5 iso, 8 anti-iso
8644⟨a, b | ab=aa, bbb=a⟩Isomorphic to ℕ(6 = 4)46 iso
8893⟨a, b | aa=a, abbb=b⟩Finite non-commutative monoid with 6 elements19 iso
81011⟨a, b | ab=a, baa=bb⟩Finite non-commutative monoid with 6 elements12 iso, 1 anti-iso
91581⟨a, b | aaa=aa, abb=b⟩Finite non-commutative monoid with 6 elements5 iso
91648⟨a, b | aab=bb, abb=a⟩Finite commutative monoid with 6 elements13 iso
91686⟨a, b | abb=aa, bbb=a⟩Isomorphic to ℕ(6 = 5)49 iso
93075⟨a, b | ab=a, aaaa=bb⟩Finite commutative monoid with 6 elements14 iso
93132⟨a, b | ab=a, bbbb=aa⟩Finite commutative monoid with 6 elements5 iso
93134⟨a, b | ab=a, bbbb=ba⟩Finite non-commutative monoid with 6 elements2 iso
93193⟨a, b | ab=a, bbb=aaa⟩Finite commutative monoid with 6 elements9 iso
93199⟨a, b | ab=a, bbb=bba⟩Finite non-commutative monoid with 6 elements3 iso
1124145⟨a, b | aa=a, abbbbba=b⟩Finite commutative monoid with 6 elements

Other isomorphic instances

The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.

66 total

Σ#PresentationMapping
91513⟨a, b | aab=ba, abab=1⟩φ(a) = b, φ(b) = a
91518⟨a, b | aab=ba, baba=1⟩φ(a) = b, φ(b) = a
91806⟨a, b | abab=1, aabba=1⟩φ(a) = b, φ(b) = a
91810⟨a, b | abab=1, abbaa=1⟩φ(a) = b, φ(b) = a
91811⟨a, b | abab=1, abbba=1⟩φ(a) = a, φ(b) = b
91815⟨a, b | abab=1, bbaaa=1⟩φ(a) = b, φ(b) = a
104889⟨a, b | aab=ba, aaabb=1⟩φ(a) = b, φ(b) = a
104892⟨a, b | aab=ba, aabba=1⟩φ(a) = b, φ(b) = a
104898⟨a, b | aab=ba, abbaa=1⟩φ(a) = b, φ(b) = a
104903⟨a, b | aab=ba, baaab=1⟩φ(a) = b, φ(b) = a
104910⟨a, b | aab=ba, bbaaa=1⟩φ(a) = b, φ(b) = a
1110701⟨a, b | aaab=aba, abab=1⟩φ(a) = b, φ(b) = a
1110706⟨a, b | aaab=aba, baba=1⟩φ(a) = b, φ(b) = a
1110836⟨a, b | aaba=baa, abab=1⟩φ(a) = b, φ(b) = a
1110841⟨a, b | aaba=baa, baba=1⟩φ(a) = b, φ(b) = a
1110916⟨a, b | aabb=aba, baba=1⟩φ(a) = a, φ(b) = b
1111020⟨a, b | abba=aab, baba=1⟩φ(a) = a, φ(b) = b
1111043⟨a, b | abba=baa, baba=1⟩φ(a) = a, φ(b) = b
1111048⟨a, b | abba=bab, baba=1⟩φ(a) = b, φ(b) = a
1111344⟨a, b | aabab=a, aabba=1⟩φ(a) = b, φ(b) = a
1111350⟨a, b | aabab=a, abbaa=1⟩φ(a) = b, φ(b) = a
1111352⟨a, b | aabab=a, abbba=1⟩φ(a) = a, φ(b) = b
1111355⟨a, b | aabab=a, baaab=1⟩φ(a) = b, φ(b) = a
1111357⟨a, b | aabab=a, baabb=1⟩φ(a) = a, φ(b) = b
1111362⟨a, b | aabab=a, bbaaa=1⟩φ(a) = b, φ(b) = a
1111363⟨a, b | aabab=a, bbaab=1⟩φ(a) = a, φ(b) = b
1111366⟨a, b | aabab=a, bbbaa=1⟩φ(a) = a, φ(b) = b
1111499⟨a, b | ababa=a, abbaa=1⟩φ(a) = b, φ(b) = a
1111501⟨a, b | ababa=a, abbba=1⟩φ(a) = a, φ(b) = b
1111504⟨a, b | ababa=a, baaab=1⟩φ(a) = b, φ(b) = a
1111506⟨a, b | ababa=a, baabb=1⟩φ(a) = a, φ(b) = b
1111572⟨a, b | abbba=b, baaab=1⟩φ(a) = b, φ(b) = a
1111579⟨a, b | abbba=b, bbaaa=1⟩φ(a) = b, φ(b) = a
1111586⟨a, b | baaab=a, baabb=1⟩φ(a) = a, φ(b) = b
1113455⟨a, b | aaabb=1, abaaba=1⟩φ(a) = b, φ(b) = a
1113473⟨a, b | aaabb=1, baabaa=1⟩φ(a) = b, φ(b) = a
1113610⟨a, b | aabba=1, aabaab=1⟩φ(a) = b, φ(b) = a
1113619⟨a, b | aabba=1, abaaba=1⟩φ(a) = b, φ(b) = a
1113637⟨a, b | aabba=1, baabaa=1⟩φ(a) = b, φ(b) = a
1113787⟨a, b | abbba=1, abbabb=1⟩φ(a) = a, φ(b) = b
1113796⟨a, b | abbba=1, babbab=1⟩φ(a) = a, φ(b) = b
1115146⟨a, b | aab=ba, aabaab=1⟩φ(a) = b, φ(b) = a
1115155⟨a, b | aab=ba, abaaba=1⟩φ(a) = b, φ(b) = a
1115173⟨a, b | aab=ba, baabaa=1⟩φ(a) = b, φ(b) = a
1116975⟨a, b | abab=1, aabbaab=1⟩φ(a) = a, φ(b) = b
1116985⟨a, b | abab=1, abaabba=1⟩φ(a) = a, φ(b) = b
1116993⟨a, b | abab=1, abbaaba=1⟩φ(a) = a, φ(b) = b
1116995⟨a, b | abab=1, abbabba=1⟩φ(a) = b, φ(b) = a
1117006⟨a, b | abab=1, baabbaa=1⟩φ(a) = a, φ(b) = b
1117013⟨a, b | abab=1, bbaabaa=1⟩φ(a) = a, φ(b) = b
1117502⟨a, b | abab=1, aabbaa=a⟩φ(a) = b, φ(b) = a
1117510⟨a, b | abab=1, abaaab=a⟩φ(a) = b, φ(b) = a
1117519⟨a, b | abab=1, abbaaa=a⟩φ(a) = b, φ(b) = a
1117521⟨a, b | abab=1, abbaab=a⟩φ(a) = a, φ(b) = b
1117524⟨a, b | abab=1, abbbaa=a⟩φ(a) = a, φ(b) = b
1117530⟨a, b | abab=1, baaaba=a⟩φ(a) = b, φ(b) = a
1117534⟨a, b | abab=1, baabba=a⟩φ(a) = a, φ(b) = b
1117539⟨a, b | abab=1, babbaa=b⟩φ(a) = b, φ(b) = a
1117540⟨a, b | abab=1, bbaaaa=a⟩φ(a) = b, φ(b) = a
1117543⟨a, b | abab=1, bbbaaa=a⟩φ(a) = a, φ(b) = b
1118033⟨a, b | abab=1, aabba=ab⟩φ(a) = a, φ(b) = b
1118040⟨a, b | abab=1, abaab=aa⟩φ(a) = b, φ(b) = a
1118042⟨a, b | abab=1, abaab=ba⟩φ(a) = a, φ(b) = b
1118050⟨a, b | abab=1, abbaa=ba⟩φ(a) = a, φ(b) = b
1118060⟨a, b | abab=1, baaba=aa⟩φ(a) = b, φ(b) = a
1118061⟨a, b | abab=1, baaba=ab⟩φ(a) = a, φ(b) = b