#5415 ⟨a, b | abbbbba=babb⟩

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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. c2ba ⇒ bc [5]
2. bab2 ⇒ cba [3]
3. bcb2 ⇒ cbc [7]
4. cbabcba ⇒ bcab2 [12]
5. cba(bc)2 ⇒ bc2b2 [13]
6. cba2b2 ⇒ babcba [6]
7. cbacb2 ⇒ ba(bc)2 [9]
8. cbcab2 ⇒ b(cb)2a [10]
9. cbc2b2 ⇒ (bc)3 [11]
10. c2b2cba ⇒ ab2cbc2 [14]
11. ab4 ⇒ c [2]
12. ab3cba ⇒ cab2 [4]
13. ab3cbc ⇒ c2b2 [8]
14. c2b4 ⇒ ab3c2bc [15]
15. c2b3abcba ⇒ ab2cbc2ab2 [16]
16. c2b3a(bc)2 ⇒ ab2cbc3b2 [17]
17. c2b3a2b2 ⇒ ab(bc)2abcba [18]
18. c2b3acb2 ⇒ ab(bc)2a(bc)2 [19]
19. c2b3cab2 ⇒ ab2(cbc)2ba [20]
20. c2b3c2b2 ⇒ ab2(cbc)2bc [21]
# ab:abbbbba=babb ac/b abbbb=c morph:5/1
ccba=bc
babb=cba
bcbb=cbc
cbabcba=bcabb
cbabcbc=bccbb
cbaabb=babcba
cbacbb=babcbc
cbcabb=bcbcba
cbccbb=bcbcbc
ccbbcba=abbcbcc
abbbb=c
abbbcba=cabb
abbbcbc=ccbb
ccbbbb=abbbccbc
ccbbbabcba=abbcbccabb
ccbbbabcbc=abbcbcccbb
ccbbbaabb=abbcbcabcba
ccbbbacbb=abbcbcabcbc
ccbbbcabb=abbcbccbcba
ccbbbccbb=abbcbccbcbc

Other submonoids of same group

11 unique, 55 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
115898⟨a, b | ababba=babab⟩Can Inf

Other submonoids of anti-isomorphic group

7 unique, 7 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
113536⟨a, b | aabaaaaaba=b⟩Can Inf