#1131 ⟨a, b | abbaab=aba⟩

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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. ba2 ⇒ c
  2. abcb ⇒ aba
  3. (cb)2 ⇒ cba
  4. abacb ⇒ ac
  5. ac2b ⇒ aca
  6. abc2 ⇒ aca
  7. cbacb ⇒ c2
  8. c3b ⇒ c2a
  9. cbc2 ⇒ c2a
  10. aca2 ⇒ abac2
  11. (ac)2b ⇒ abac2
  12. c2a2 ⇒ cbac2
  13. c2acb ⇒ cbac2
  14. abac2a ⇒ ac3
  15. ac3a ⇒ acac2
  16. cbac2a ⇒ c4
  17. c4a ⇒ c2ac2
  18. acac2a ⇒ abac4
  19. (c2a)2 ⇒ cbac4 
# ab:abbaab=aba b/ac baa=c frequency:3/2
baa=c
abcb=aba
cbcb=cba
abacb=ac
accb=aca
abcc=aca
cbacb=cc
cccb=cca
cbcc=cca
acaa=abacc
acacb=abacc
ccaa=cbacc
ccacb=cbacc
abacca=accc
accca=acacc
cbacca=cccc
cccca=ccacc
acacca=abacccc
ccacca=cbacccc

Right Cayley graph (truncated)

Left Cayley graph (truncated)