#1525 ⟨a, b | ababbbbaba=1⟩

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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. bc ⇒ cb
  2. b4 ⇒ c
  3. dc ⇒ 1
  4. cd ⇒ 1
  5. bd ⇒ db
  6. caba ⇒ abac
  7. c(ba)2 ⇒ (ba)2c
  8. cb(ba)2 ⇒ b(ba)2c
  9. cb3aba ⇒ b3abac
  10. daba ⇒ abad
  11. d(ba)2 ⇒ (ba)2d
  12. db(ba)2 ⇒ b(ba)2d
  13. db3aba ⇒ b3abad
  14. ba2ba ⇒ abacadb
  15. b3aba2 ⇒ a2bab3
  16. b3abaca ⇒ ca2bab3
  17. b3abac2a ⇒ c2a2bab3
  18. b3abac3a ⇒ c3a2bab3
  19. c4a2ba ⇒ b3abac4adb
  20. da2ba ⇒ b3ab(ad)2b
  21. a2baca ⇒ db3 
# ab:ababbbbaba=1 cb/d/a bbbb=c,abaaba=d magic:1
bc=cb
bbbb=c
dc=1
cd=1
bd=db
caba=abac
cbaba=babac
cbbaba=bbabac
cbbbaba=bbbabac
daba=abad
dbaba=babad
dbbaba=bbabad
dbbbaba=bbbabad
baaba=abacadb
bbbabaa=aababbb
bbbabaca=caababbb
bbbabacca=ccaababbb
bbbabaccca=cccaababbb
ccccaaba=bbbabaccccadb
daaba=bbbabadadb
aabaca=dbbb

Right Cayley graph (truncated)

Left Cayley graph (truncated)