#3536 ⟨a, b | aabaaaaaba=b⟩

Up:Monoid enumeration
Prev:#3535 ⟨a, b | aabaaaaaba=a⟩
Next:#3537 ⟨a, b | aabaaaaabb=a⟩

Contents

  1. Properties
  2. Rewriting system
  3. Other submonoids of same group
  4. Other submonoids of anti-isomorphic group

Properties

Rewriting system

Format:
Word:
Enter a word above to compute its normal form. Tips:
  • Lowercase letters stand for generators.
  • Spaces are ignored.
  • Numbers repeat the previous letter, e.g. b90.
Strategy:
Result: 1 
1
#RuleProof
1. cbab ⇒ bc2bc3ba [13]
2. cbcab ⇒ bc2ba [10]
3. ac ⇒ ca [4]
4. c2bc2ab2 ⇒ bc2b(c3b)2a [16]
5. cbc2abc ⇒ ba [5]
6. a2 ⇒ c [2]
7. cbc2aba ⇒ b [3]
8. b(ab)2 ⇒ cbc2ab2c2bc3ba [15]
9. c(ab)2 ⇒ abc2bc3ba [14]
10. babcab ⇒ cbc2ab2c2ba [12]
11. (cab)2 ⇒ abc2ba [11]
12. bcabc2ab2 ⇒ cbc2ab2c2b(c3b)2a [18]
13. (c2ab)2b ⇒ abc2b(c3b)2a [17]
14. babc2abc ⇒ cbc2ab2a [9]
15. (cabc)2 ⇒ aba [7]
16. babc2aba ⇒ cbc2ab2 [8]
17. cabc2aba ⇒ ab [6]
# ab:aabaaaaaba=b reversed:bc/a aa=c morph:2/0
cbab=bccbcccba
cbcab=bccba
ac=ca
ccbccabb=bccbcccbcccba
cbccabc=ba
aa=c
cbccaba=b
babab=cbccabbccbcccba
cabab=abccbcccba
babcab=cbccabbccba
cabcab=abccba
bcabccabb=cbccabbccbcccbcccba
ccabccabb=abccbcccbcccba
babccabc=cbccabba
cabccabc=aba
babccaba=cbccabb
cabccaba=ab

Other submonoids of same group

12 unique, 56 total

Σ#PresentationPropertiesφ
6104⟨a, b | aaba=bb⟩Can Inf
7145⟨a, b | aababba=1⟩Grp Inf44
7193⟨a, b | ababba=b⟩Can Inf
7252⟨a, b | aaba=bab⟩Can Inf
9842⟨a, b | abaababa=b⟩Can Inf
91126⟨a, b | ababba=bab⟩Can Inf
91273⟨a, b | abbba=babb⟩Can Inf
102633⟨a, b | abbbba=babb⟩Can Inf
113716⟨a, b | abaaabaaba=b⟩Can Inf
114876⟨a, b | abbabbba=bab⟩Can Inf
115415⟨a, b | abbbbba=babb⟩Can Inf
115898⟨a, b | ababba=babab⟩Can Inf

Other submonoids of anti-isomorphic group

6 unique, 6 total

Σ#PresentationProperties
687⟨a, b | aabba=b⟩Can Inf
7179⟨a, b | aababa=b⟩Can Inf
8374⟨a, b | aabaaba=b⟩Can Inf
8586⟨a, b | baab=aaba⟩Can Inf
9792⟨a, b | aabaaaba=b⟩Can Inf
101666⟨a, b | aabaaaaba=b⟩Can Inf