#2565 ⟨a, b | abaaab=aaba⟩

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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. dc ⇒ ad
  2. aca ⇒ d
  3. ada ⇒ acd
  4. ba2 ⇒ c
  5. cba ⇒ bdb
  6. c2a ⇒ bad
  7. cda ⇒ c2d
  8. dba ⇒ a2c
  9. d2a ⇒ ad2
  10. a2ba ⇒ db
  11. ad2b ⇒ abd2
  12. caba ⇒ badb
  13. c2db ⇒ bdac
  14. cd2b ⇒ cbd2
  15. daba ⇒ acdb
  16. dbca ⇒ a2bd
  17. dbda ⇒ dbcd
  18. (db)2 ⇒ a3c
  19. d3b ⇒ dbd2
  20. a2cdb ⇒ dac
  21. abadb ⇒ a2c
  22. cacdb ⇒ bd2
  23. dacdb ⇒ abad2
  24. dbd2b ⇒ db2d2
  25. db2adb ⇒ a2c2 
# ab:abaaab=aaba abcd baa=c,aca=d frequency:3/3,3/0
dc=ad
aca=d
ada=acd
baa=c
cba=bdb
cca=bad
cda=ccd
dba=aac
dda=add
aaba=db
addb=abdd
caba=badb
ccdb=bdac
cddb=cbdd
daba=acdb
dbca=aabd
dbda=dbcd
dbdb=aaac
dddb=dbdd
aacdb=dac
abadb=aac
cacdb=bdd
dacdb=abadd
dbddb=dbbdd
dbbadb=aacc

Right Cayley graph (truncated)

Left Cayley graph (truncated)