#267 ⟨a, b | abba=bab⟩

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Contents

  1. Properties
  2. Rewriting system
  3. Other submonoids of same 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. cd ⇒ db [6]
2. ad ⇒ cb [5]
3. bc ⇒ d [3]
4. ba ⇒ c [2]
5. bd2 ⇒ d2c [9]
6. bdc ⇒ d2a [8]
7. bdb ⇒ d2 [7]
# ab:abba=bab dcab ba=c,bc=d morph:2/1,2/0
cd=db
ad=cb
bc=d
ba=c
bdd=ddc
bdc=dda
bdb=dd

Other submonoids of same group

12 unique, 57 total

Σ#PresentationPropertiesφ
530⟨a, b | aabba=1⟩Grp Inf40
543⟨a, b | abba=b⟩Can Inf
546⟨a, b | aaa=bb⟩Can Inf
553⟨a, b | aba=bb⟩Can Inf
691⟨a, b | ababa=b⟩Can Inf5
6123⟨a, b | bab=aba⟩Can Inf
8555⟨a, b | abbba=bab⟩Can Inf
91137⟨a, b | abbbba=bab⟩Can Inf
91262⟨a, b | ababa=baab⟩Can Inf
102361⟨a, b | abbbbba=bab⟩Can Inf
114887⟨a, b | abbbbbba=bab⟩Can Inf
115855⟨a, b | abaaba=baaab⟩Can Inf