#2009 ⟨a, b | aabbbbaa=ab⟩

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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. ab2 ⇒ c
  2. cb3 ⇒ c2b2ac
  3. acb2ac ⇒ cb
  4. c2b2a2 ⇒ cb
  5. c2b2(ac)2 ⇒ acb2cb
  6. cbcb2ac ⇒ c2b2acb
  7. acb2a2 ⇒ ab
  8. abcb2ac ⇒ cb2
  9. c2b2aca2 ⇒ acb2ab
  10. c2b(bac)2 ⇒ a(bcb)2
  11. cbcb2a2 ⇒ cb2
  12. (cb2)2ac ⇒ c2b2acb2
  13. abcb2a2 ⇒ c
  14. c2b2acba2 ⇒ abcb2ab
  15. (cb2)2a2 ⇒ c2b2ac 
# ab:aabbbbaa=ab c/ab abb=c frequency:3/2
abb=c
cbbb=ccbbac
acbbac=cb
ccbbaa=cb
ccbbacac=acbbcb
cbcbbac=ccbbacb
acbbaa=ab
abcbbac=cbb
ccbbacaa=acbbab
ccbbacbac=abcbbcb
cbcbbaa=cbb
cbbcbbac=ccbbacbb
abcbbaa=c
ccbbacbaa=abcbbab
cbbcbbaa=ccbbac

Right Cayley graph (truncated)

Left Cayley graph (truncated)