#21739 ⟨a, b | aaa=1, abbabba=b⟩

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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. db2 ⇒ b
  2. bd ⇒ db
  3. d2b ⇒ d
  4. cdb ⇒ c
  5. b3c ⇒ cb3
  6. dc ⇒ b2cd3
  7. dbc ⇒ c
  8. ab ⇒ cd
  9. ad ⇒ cd3
  10. ba ⇒ bcd2
  11. da ⇒ b2cd5
  12. (bc)2 ⇒ c2b5
  13. b2c2 ⇒ cbcd2
  14. ca ⇒ c2d2
  15. ac ⇒ cbcd3
  16. c3 ⇒ b3
  17. a3 ⇒ 1 
# ab:aaa=1,abbabba=b b/d/ca abb=c,cabcabca=d frequency:3/2,8/0
dbb=b
bd=db
ddb=d
cdb=c
bbbc=cbbb
dc=bbcddd
dbc=c
ab=cd
ad=cddd
ba=bcdd
da=bbcddddd
bcbc=ccbbbbb
bbcc=cbcdd
ca=ccdd
ac=cbcddd
ccc=bbb
aaa=1

Right Cayley graph (truncated)

Left Cayley graph (truncated)