#1524 ⟨a, b | ababbbbaab=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. dc ⇒ 1
  2. cd ⇒ 1
  3. cb ⇒ bc
  4. db ⇒ bd
  5. b4 ⇒ c
  6. a2b ⇒ bdaca
  7. acab3 ⇒ b3a2c
  8. a(ba)2c ⇒ (ba)2ca
  9. abacad ⇒ b3da(ba)2
  10. (ab)3c ⇒ (ba)2cab
  11. abacabd ⇒ b3d(ab)3
  12. (ab)3bc ⇒ (ba)2cab2
  13. abacab2d ⇒ b3d(ab)3b
  14. (ab)3b2 ⇒ baca2
  15. abaca2 ⇒ b3d
  16. (aca)2d ⇒ b3ab3da(ba)2
  17. (aca)2bd ⇒ b3ab3d(ab)3
  18. (aca)2b2d ⇒ b3ab3d(ab)3b
  19. a(ca2)2 ⇒ b3ab3d 
# ab:ababbbbaab=1 reversed:cdb/a bbbb=c,aababa=d magic:1
dc=1
cd=1
cb=bc
db=bd
bbbb=c
aab=bdaca
acabbb=bbbaac
ababac=babaca
abacad=bbbdababa
abababc=babacab
abacabd=bbbdababab
abababbc=babacabb
abacabbd=bbbdabababb
abababbb=bacaa
abacaa=bbbd
acaacad=bbbabbbdababa
acaacabd=bbbabbbdababab
acaacabbd=bbbabbbdabababb
acaacaa=bbbabbbd

Right Cayley graph (truncated)

Left Cayley graph (truncated)