#696 ⟨a, b | abaaaaaba=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. c2b ⇒ bc2
  2. ac3 ⇒ b
  3. c2a ⇒ ac2
  4. abc ⇒ bca
  5. acb ⇒ bac
  6. acac2 ⇒ ba
  7. b(cb)2 ⇒ c9
  8. (bc)2a ⇒ c6
  9. bcab ⇒ c5
  10. bca2 ⇒ c2
  11. ab2 ⇒ bc(ac)2
  12. abac2 ⇒ b(ca)2
  13. a2b ⇒ c
  14. acab ⇒ ba2c
  15. a3c2 ⇒ 1
  16. aca2c2 ⇒ ba2
  17. ca3 ⇒ a3c
  18. ba3 ⇒ ac
  19. (ab)2 ⇒ bcaca2c
  20. aba2c2 ⇒ bcaca2 
# ab:abaaaaaba=1 c/ba aab=c frequency:3/2
ccb=bcc
accc=b
cca=acc
abc=bca
acb=bac
acacc=ba
bcbcb=ccccccccc
bcbca=cccccc
bcab=ccccc
bcaa=cc
abb=bcacac
abacc=bcaca
aab=c
acab=baac
aaacc=1
acaacc=baa
caaa=aaac
baaa=ac
abab=bcacaac
abaacc=bcacaa

Right Cayley graph (truncated)

Left Cayley graph (truncated)