#2345 ⟨a, b | abbaaab=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. abcb ⇒ aba
  2. (cb)2 ⇒ cba
  3. ba3 ⇒ c
  4. abacb ⇒ aba2
  5. ac2b ⇒ aca
  6. abc2 ⇒ aca
  7. cbacb ⇒ cba2
  8. c3b ⇒ c2a
  9. cbc2 ⇒ c2a
  10. aba2cb ⇒ ac
  11. aca2 ⇒ abac2
  12. (ac)2b ⇒ abac2
  13. cba2cb ⇒ c2
  14. c2a2 ⇒ cbac2
  15. c2acb ⇒ cbac2
  16. abac2a ⇒ aba2c2
  17. ac3a ⇒ acac2
  18. cbac2a ⇒ cba2c2
  19. c4a ⇒ c2ac2
  20. aba2c2a ⇒ ac3
  21. acac2a ⇒ abac4
  22. cba2c2a ⇒ c4
  23. (c2a)2 ⇒ cbac4 
# ab:abbaaab=aba b/ac baaa=c frequency:4/2
abcb=aba
cbcb=cba
baaa=c
abacb=abaa
accb=aca
abcc=aca
cbacb=cbaa
cccb=cca
cbcc=cca
abaacb=ac
acaa=abacc
acacb=abacc
cbaacb=cc
ccaa=cbacc
ccacb=cbacc
abacca=abaacc
accca=acacc
cbacca=cbaacc
cccca=ccacc
abaacca=accc
acacca=abacccc
cbaacca=cccc
ccacca=cbacccc

Right Cayley graph (truncated)

Left Cayley graph (truncated)