#1415 ⟨a, b | aababaaaab=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. cd ⇒ dc
  2. ad ⇒ da
  3. ac ⇒ ca
  4. a2 ⇒ c
  5. dc2 ⇒ 1
  6. (cb)2 ⇒ babca
  7. (ab)2 ⇒ bc2bdc
  8. abc2b ⇒ cbabc
  9. dcbab ⇒ bcbda
  10. dcbc2b ⇒ abcbdca
  11. cabcb ⇒ bc2ba
  12. bcbab ⇒ d
  13. cb2ab ⇒ babc2abda
  14. ab2c2b ⇒ bc2bdcabc
  15. dcb2c2b ⇒ bcbdcbc
  16. cab2ab ⇒ bc2bcabda
  17. bcb2c2b ⇒ dabc
  18. cb3c2b ⇒ babc2abdcbc
  19. cab3c2b ⇒ bc2bcabdcbc 
# ab:aababaaaab=1 dca/b aa=c,bcbab=d frequency:2/0,5/0
cd=dc
ad=da
ac=ca
aa=c
dcc=1
cbcb=babca
abab=bccbdc
abccb=cbabc
dcbab=bcbda
dcbccb=abcbdca
cabcb=bccba
bcbab=d
cbbab=babccabda
abbccb=bccbdcabc
dcbbccb=bcbdcbc
cabbab=bccbcabda
bcbbccb=dabc
cbbbccb=babccabdcbc
cabbbccb=bccbcabdcbc

Right Cayley graph (truncated)

Left Cayley graph (truncated)