#2044 ⟨a, b | abaabbab=ba⟩

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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. (c2b)2bab ⇒ bac
  2. acb2ab ⇒ ba
  3. acb2ac ⇒ ca
  4. acbc2b2ab ⇒ c
  5. ba2 ⇒ c
  6. (ba)2 ⇒ c2b2ab
  7. baca ⇒ c2b2ac
  8. ca2 ⇒ acbc2b2ac
  9. cab2ab ⇒ acb3a
  10. cab2ac ⇒ acb2ca
  11. cabc2b2ab ⇒ acb2c
  12. c2(b2a)2 ⇒ bac2b2ab
  13. c2b2abca ⇒ bac2b2ac
  14. c(cb2ab)2 ⇒ bab2a
  15. c2b2abcb2ac ⇒ babca
  16. (c2b2a)2b ⇒ bacba
  17. (c2b2a)2c ⇒ bac2a
  18. c2b2abcbc2b2ab ⇒ babc 
# ab:abaabbab=ba bc/a baa=c frequency:3/0
ccbccbbab=bac
acbbab=ba
acbbac=ca
acbccbbab=c
baa=c
baba=ccbbab
baca=ccbbac
caa=acbccbbac
cabbab=acbbba
cabbac=acbbca
cabccbbab=acbbc
ccbbabba=baccbbab
ccbbabca=baccbbac
ccbbabcbbab=babba
ccbbabcbbac=babca
ccbbaccbbab=bacba
ccbbaccbbac=bacca
ccbbabcbccbbab=babc

Right Cayley graph (truncated)

Left Cayley graph (truncated)