#19818 ⟨a, b | aaa=a, abba=bab⟩

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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. a3 ⇒ a
  2. a2c ⇒ c
  3. ab ⇒ c
  4. c2a2 ⇒ c2
  5. cba ⇒ ac2
  6. bc ⇒ ac2
  7. c2aca2 ⇒ c2ac
  8. cac2 ⇒ c(ca)2
  9. ac2ac ⇒ c(ca)2
  10. c2b ⇒ c2ac
  11. bac2 ⇒ c2ac
  12. c2(ac)2 ⇒ c4a
  13. ac4 ⇒ c3ac
  14. ac3ac ⇒ c4
  15. c2acb ⇒ c4a 
# ab:aaa=a,abba=bab a/cb ab=c frequency:2/0
aaa=a
aac=c
ab=c
ccaa=cc
cba=acc
bc=acc
ccacaa=ccac
cacc=ccaca
accac=ccaca
ccb=ccac
bacc=ccac
ccacac=cccca
acccc=cccac
acccac=cccc
ccacb=cccca

Right Cayley graph (truncated)

Left Cayley graph (truncated)