#16 ⟨a, b | aa=1, bbb=1⟩

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Properties

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. a2 ⇒ 1
  2. b3 ⇒ 1 
# ab:aa=1,bbb=1 ab
aa=1
bbb=1

Right Cayley graph (truncated)

Left Cayley graph (truncated)

Other isomorphic instances

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

146 total

Σ#PresentationMapping
7130⟨a, b | aab=b, bbb=1⟩φ(a) = a, φ(b) = b
7290⟨a, b | aa=1, aabbb=1⟩φ(a) = a, φ(b) = b
7295⟨a, b | aa=1, abbba=1⟩φ(a) = a, φ(b) = b
7298⟨a, b | aa=1, baabb=1⟩φ(a) = a, φ(b) = b
7331⟨a, b | aa=1, abbb=a⟩φ(a) = a, φ(b) = b
7372⟨a, b | aa=1, bbb=aa⟩φ(a) = a, φ(b) = b
8667⟨a, b | aaa=1, aaabb=1⟩φ(a) = b, φ(b) = a
8670⟨a, b | aaa=1, aabba=1⟩φ(a) = b, φ(b) = a
8678⟨a, b | aaa=1, baaab=1⟩φ(a) = b, φ(b) = a
91843⟨a, b | aaa=a, aabbb=1⟩φ(a) = a, φ(b) = b
91848⟨a, b | aaa=a, abbba=1⟩φ(a) = a, φ(b) = b
91851⟨a, b | aaa=a, baabb=1⟩φ(a) = a, φ(b) = b
91915⟨a, b | aab=b, aabbb=1⟩φ(a) = a, φ(b) = b
91922⟨a, b | aab=b, abbba=1⟩φ(a) = a, φ(b) = b
91927⟨a, b | aab=b, baabb=1⟩φ(a) = a, φ(b) = b
91933⟨a, b | aab=b, bbaab=1⟩φ(a) = a, φ(b) = b
91936⟨a, b | aab=b, bbbaa=1⟩φ(a) = a, φ(b) = b
92571⟨a, b | aaa=1, aabb=aa⟩φ(a) = b, φ(b) = a
92579⟨a, b | aaa=1, abba=aa⟩φ(a) = b, φ(b) = a
93207⟨a, b | aa=1, aaaabbb=1⟩φ(a) = a, φ(b) = b
93214⟨a, b | aa=1, aaabbba=1⟩φ(a) = a, φ(b) = b
93218⟨a, b | aa=1, aabaabb=1⟩φ(a) = a, φ(b) = b
93223⟨a, b | aa=1, aabbaab=1⟩φ(a) = a, φ(b) = b
93226⟨a, b | aa=1, aabbbaa=1⟩φ(a) = a, φ(b) = b
93234⟨a, b | aa=1, abaabba=1⟩φ(a) = a, φ(b) = b
93253⟨a, b | aa=1, baaaabb=1⟩φ(a) = a, φ(b) = b
93256⟨a, b | aa=1, baabaab=1⟩φ(a) = a, φ(b) = b
93350⟨a, b | aa=1, aaabbb=a⟩φ(a) = a, φ(b) = b
93362⟨a, b | aa=1, aabbba=a⟩φ(a) = a, φ(b) = b
93370⟨a, b | aa=1, abaabb=a⟩φ(a) = a, φ(b) = b
93378⟨a, b | aa=1, abbaab=a⟩φ(a) = a, φ(b) = b
93498⟨a, b | aa=1, aabbb=aa⟩φ(a) = a, φ(b) = b
93517⟨a, b | aa=1, abbba=aa⟩φ(a) = a, φ(b) = b
93527⟨a, b | aa=1, baabb=aa⟩φ(a) = a, φ(b) = b
93613⟨a, b | aa=1, aaaa=bbb⟩φ(a) = a, φ(b) = b
93652⟨a, b | aa=1, abbb=aaa⟩φ(a) = a, φ(b) = b
104345⟨a, b | aaaa=a, aaabb=1⟩φ(a) = b, φ(b) = a
104348⟨a, b | aaaa=a, aabba=1⟩φ(a) = b, φ(b) = a
104356⟨a, b | aaaa=a, baaab=1⟩φ(a) = b, φ(b) = a
104417⟨a, b | aaab=b, aaabb=1⟩φ(a) = b, φ(b) = a
104420⟨a, b | aaab=b, aabba=1⟩φ(a) = b, φ(b) = a
104426⟨a, b | aaab=b, abbaa=1⟩φ(a) = b, φ(b) = a
104431⟨a, b | aaab=b, baaab=1⟩φ(a) = b, φ(b) = a
104438⟨a, b | aaab=b, bbaaa=1⟩φ(a) = b, φ(b) = a
107486⟨a, b | aaa=1, aaaabb=a⟩φ(a) = b, φ(b) = a
107492⟨a, b | aaa=1, aaabba=a⟩φ(a) = b, φ(b) = a
107502⟨a, b | aaa=1, aabbaa=a⟩φ(a) = b, φ(b) = a
107510⟨a, b | aaa=1, abaaab=a⟩φ(a) = b, φ(b) = a
108027⟨a, b | aaa=1, aaaa=abb⟩φ(a) = b, φ(b) = a
1111627⟨a, b | aaaa=aa, aabbb=1⟩φ(a) = a, φ(b) = b
1111632⟨a, b | aaaa=aa, abbba=1⟩φ(a) = a, φ(b) = b
1111635⟨a, b | aaaa=aa, baabb=1⟩φ(a) = a, φ(b) = b
1111731⟨a, b | aaab=ab, aabbb=1⟩φ(a) = a, φ(b) = b
1111738⟨a, b | aaab=ab, abbba=1⟩φ(a) = a, φ(b) = b
1111743⟨a, b | aaab=ab, baabb=1⟩φ(a) = a, φ(b) = b
1111749⟨a, b | aaab=ab, bbaab=1⟩φ(a) = a, φ(b) = b
1111752⟨a, b | aaab=ab, bbbaa=1⟩φ(a) = a, φ(b) = b
1111891⟨a, b | aaba=ba, aabbb=1⟩φ(a) = a, φ(b) = b
1111898⟨a, b | aaba=ba, abbba=1⟩φ(a) = a, φ(b) = b
1111903⟨a, b | aaba=ba, baabb=1⟩φ(a) = a, φ(b) = b
1111909⟨a, b | aaba=ba, bbaab=1⟩φ(a) = a, φ(b) = b
1111912⟨a, b | aaba=ba, bbbaa=1⟩φ(a) = a, φ(b) = b
1111951⟨a, b | aabb=aa, aaabb=1⟩φ(a) = b, φ(b) = a
1111954⟨a, b | aabb=aa, aabba=1⟩φ(a) = b, φ(b) = a
1111960⟨a, b | aabb=aa, abbaa=1⟩φ(a) = b, φ(b) = a
1111965⟨a, b | aabb=aa, baaab=1⟩φ(a) = b, φ(b) = a
1111972⟨a, b | aabb=aa, bbaaa=1⟩φ(a) = b, φ(b) = a
1112079⟨a, b | abba=aa, aaabb=1⟩φ(a) = b, φ(b) = a
1112082⟨a, b | abba=aa, aabba=1⟩φ(a) = b, φ(b) = a
1112090⟨a, b | abba=aa, baaab=1⟩φ(a) = b, φ(b) = a
1118151⟨a, b | aaa=a, aaaabbb=1⟩φ(a) = a, φ(b) = b
1118158⟨a, b | aaa=a, aaabbba=1⟩φ(a) = a, φ(b) = b
1118162⟨a, b | aaa=a, aabaabb=1⟩φ(a) = a, φ(b) = b
1118167⟨a, b | aaa=a, aabbaab=1⟩φ(a) = a, φ(b) = b
1118170⟨a, b | aaa=a, aabbbaa=1⟩φ(a) = a, φ(b) = b
1118178⟨a, b | aaa=a, abaabba=1⟩φ(a) = a, φ(b) = b
1118197⟨a, b | aaa=a, baaaabb=1⟩φ(a) = a, φ(b) = b
1118200⟨a, b | aaa=a, baabaab=1⟩φ(a) = a, φ(b) = b
1118423⟨a, b | aab=b, aaaabbb=1⟩φ(a) = a, φ(b) = b
1118430⟨a, b | aab=b, aaabbba=1⟩φ(a) = a, φ(b) = b
1118435⟨a, b | aab=b, aabaabb=1⟩φ(a) = a, φ(b) = b
1118441⟨a, b | aab=b, aabbaab=1⟩φ(a) = a, φ(b) = b
1118444⟨a, b | aab=b, aabbbaa=1⟩φ(a) = a, φ(b) = b
1118454⟨a, b | aab=b, abaabba=1⟩φ(a) = a, φ(b) = b
1118466⟨a, b | aab=b, abbaaba=1⟩φ(a) = a, φ(b) = b
1118472⟨a, b | aab=b, abbbaaa=1⟩φ(a) = a, φ(b) = b
1118483⟨a, b | aab=b, baaaabb=1⟩φ(a) = a, φ(b) = b
1118489⟨a, b | aab=b, baabaab=1⟩φ(a) = a, φ(b) = b
1118492⟨a, b | aab=b, baabbaa=1⟩φ(a) = a, φ(b) = b
1118513⟨a, b | aab=b, bbaaaab=1⟩φ(a) = a, φ(b) = b
1118516⟨a, b | aab=b, bbaabaa=1⟩φ(a) = a, φ(b) = b
1118528⟨a, b | aab=b, bbbaaaa=1⟩φ(a) = a, φ(b) = b
1121123⟨a, b | aaa=1, aaaaaabb=1⟩φ(a) = b, φ(b) = a
1121126⟨a, b | aaa=1, aaaaabba=1⟩φ(a) = b, φ(b) = a
1121132⟨a, b | aaa=1, aaaabbaa=1⟩φ(a) = b, φ(b) = a
1121136⟨a, b | aaa=1, aaabaaab=1⟩φ(a) = b, φ(b) = a
1121143⟨a, b | aaa=1, aaabbaaa=1⟩φ(a) = b, φ(b) = a
1121152⟨a, b | aaa=1, aabaaaba=1⟩φ(a) = b, φ(b) = a
1121220⟨a, b | aaa=1, baaaaaab=1⟩φ(a) = b, φ(b) = a
1122194⟨a, b | aaa=1, aaaaaa=bb⟩φ(a) = b, φ(b) = a
1122742⟨a, b | aaa=1, aaabb=aaa⟩φ(a) = b, φ(b) = a
1122764⟨a, b | aaa=1, aabba=aaa⟩φ(a) = b, φ(b) = a
1122824⟨a, b | aaa=1, baaab=aaa⟩φ(a) = b, φ(b) = a
1125919⟨a, b | aa=1, aaaaaabbb=1⟩φ(a) = a, φ(b) = b
1125926⟨a, b | aa=1, aaaaabbba=1⟩φ(a) = a, φ(b) = b
1125931⟨a, b | aa=1, aaaabaabb=1⟩φ(a) = a, φ(b) = b
1125937⟨a, b | aa=1, aaaabbaab=1⟩φ(a) = a, φ(b) = b
1125940⟨a, b | aa=1, aaaabbbaa=1⟩φ(a) = a, φ(b) = b
1125949⟨a, b | aa=1, aaabaabba=1⟩φ(a) = a, φ(b) = b
1125960⟨a, b | aa=1, aaabbaaba=1⟩φ(a) = a, φ(b) = b
1125966⟨a, b | aa=1, aaabbbaaa=1⟩φ(a) = a, φ(b) = b
1125976⟨a, b | aa=1, aabaaaabb=1⟩φ(a) = a, φ(b) = b
1125981⟨a, b | aa=1, aabaabaab=1⟩φ(a) = a, φ(b) = b
1125984⟨a, b | aa=1, aabaabbaa=1⟩φ(a) = a, φ(b) = b
1126002⟨a, b | aa=1, aabbaaaab=1⟩φ(a) = a, φ(b) = b
1126032⟨a, b | aa=1, abaaaabba=1⟩φ(a) = a, φ(b) = b
1126041⟨a, b | aa=1, abaabaaba=1⟩φ(a) = a, φ(b) = b
1126113⟨a, b | aa=1, baaaaaabb=1⟩φ(a) = a, φ(b) = b
1126116⟨a, b | aa=1, baaaabaab=1⟩φ(a) = a, φ(b) = b
1126454⟨a, b | aa=1, aaaaabbb=a⟩φ(a) = a, φ(b) = b
1126468⟨a, b | aa=1, aaaabbba=a⟩φ(a) = a, φ(b) = b
1126476⟨a, b | aa=1, aaabaabb=a⟩φ(a) = a, φ(b) = b
1126488⟨a, b | aa=1, aaabbaab=a⟩φ(a) = a, φ(b) = b
1126494⟨a, b | aa=1, aaabbbaa=a⟩φ(a) = a, φ(b) = b
1126512⟨a, b | aa=1, aabaabba=a⟩φ(a) = a, φ(b) = b
1126532⟨a, b | aa=1, aabbaaba=a⟩φ(a) = a, φ(b) = b
1126560⟨a, b | aa=1, abaaaabb=a⟩φ(a) = a, φ(b) = b
1126568⟨a, b | aa=1, abaabaab=a⟩φ(a) = a, φ(b) = b
1126602⟨a, b | aa=1, abbaaaab=a⟩φ(a) = a, φ(b) = b
1126995⟨a, b | aa=1, aaaabbb=aa⟩φ(a) = a, φ(b) = b
1127022⟨a, b | aa=1, aaabbba=aa⟩φ(a) = a, φ(b) = b
1127038⟨a, b | aa=1, aabaabb=aa⟩φ(a) = a, φ(b) = b
1127057⟨a, b | aa=1, aabbaab=aa⟩φ(a) = a, φ(b) = b
1127069⟨a, b | aa=1, aabbbaa=aa⟩φ(a) = a, φ(b) = b
1127099⟨a, b | aa=1, abaabba=aa⟩φ(a) = a, φ(b) = b
1127171⟨a, b | aa=1, baaaabb=aa⟩φ(a) = a, φ(b) = b
1127183⟨a, b | aa=1, baabaab=aa⟩φ(a) = a, φ(b) = b
1127501⟨a, b | aa=1, aaaaaa=bbb⟩φ(a) = a, φ(b) = b
1127550⟨a, b | aa=1, aaabbb=aaa⟩φ(a) = a, φ(b) = b
1127596⟨a, b | aa=1, aabbba=aaa⟩φ(a) = a, φ(b) = b
1127626⟨a, b | aa=1, abaabb=aaa⟩φ(a) = a, φ(b) = b
1127658⟨a, b | aa=1, abbaab=aaa⟩φ(a) = a, φ(b) = b
1128030⟨a, b | aa=1, aaaaa=abbb⟩φ(a) = a, φ(b) = b
1128124⟨a, b | aa=1, aabbb=aaaa⟩φ(a) = a, φ(b) = b
1128198⟨a, b | aa=1, abbba=aaaa⟩φ(a) = a, φ(b) = b
1128234⟨a, b | aa=1, baabb=aaaa⟩φ(a) = a, φ(b) = b