#1783 ⟨a, b | abababaab=a⟩

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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. ba ⇒ c
  2. c4ab ⇒ c
  3. c4ac ⇒ ca
  4. ca2b ⇒ c10a
  5. (ca)2b ⇒ c7a
  6. cac2ab ⇒ c4a
  7. ac3ab ⇒ a
  8. ca2c ⇒ c10a2
  9. c(ac)2 ⇒ c7a2
  10. (cac)2 ⇒ c4a2
  11. ac3ac ⇒ a2
  12. a3b ⇒ ac9a
  13. a2cab ⇒ ac6a
  14. a2c2ab ⇒ ac3a
  15. a3c ⇒ ac9a2
  16. a(ac)2 ⇒ ac6a2
  17. a2c2ac ⇒ ac3a2 
# ab:abababaab=a reversed:bc/a ba=c frequency:2/1
ba=c
ccccab=c
ccccac=ca
caab=cccccccccca
cacab=ccccccca
caccab=cccca
acccab=a
caac=ccccccccccaa
cacac=cccccccaa
caccac=ccccaa
acccac=aa
aaab=accccccccca
aacab=acccccca
aaccab=accca
aaac=acccccccccaa
aacac=accccccaa
aaccac=acccaa

Right Cayley graph (truncated)

Left Cayley graph (truncated)