#2265 ⟨a, b | aabbaba=baa⟩

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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. bd ⇒ dcb
  2. bc2 ⇒ d2cbc
  3. bcd ⇒ d(dc)2b
  4. bca ⇒ d2cba
  5. bac ⇒ dc
  6. bad ⇒ d2
  7. acdc ⇒ dac
  8. acd2 ⇒ dad
  9. a(dc)2 ⇒ cac
  10. adcd2 ⇒ cad
  11. acb ⇒ d
  12. adcbc ⇒ c2
  13. ab2c ⇒ cb2a
  14. ba2 ⇒ da
  15. acda ⇒ da2
  16. adcda ⇒ ca2
  17. adcba ⇒ ca
  18. ab2a ⇒ c 
# ab:aabbaba=baa reversed:cd/b/a abba=c,acb=d frequency:4/1,3/2
bd=dcb
bcc=ddcbc
bcd=ddcdcb
bca=ddcba
bac=dc
bad=dd
acdc=dac
acdd=dad
adcdc=cac
adcdd=cad
acb=d
adcbc=cc
abbc=cbba
baa=da
acda=daa
adcda=caa
adcba=ca
abba=c

Right Cayley graph (truncated)

Left Cayley graph (truncated)