#5898 ⟨a, b | ababba=babab⟩

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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. abac ⇒ cb [3]
2. abab2a ⇒ b(ab)2 [1]
3. b(ba)2 ⇒ c [2]
4. bcb ⇒ cb2a [4]
5. bc2 ⇒ c2ba [6]
6. b2acb ⇒ cbab2a [5]
7. b2ac2 ⇒ (cba)2 [7]
# ab:ababba=babab reversed:a/bc bbaba=c morph:5/1
abac=cb
ababba=babab
bbaba=c
bcb=cbba
bcc=ccba
bbacb=cbabba
bbacc=cbacba

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
115415⟨a, b | abbbbba=babb⟩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