#1516 ⟨a, b | abababbbba=1⟩

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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. bc ⇒ cb
  2. cb4 ⇒ 1
  3. cbab4a ⇒ a2b
  4. cb2ab4a ⇒ ba2b
  5. b3a2 ⇒ ab4acb3
  6. cb3ab4a ⇒ b2a2b
  7. ca(ba)2 ⇒ a2bacb
  8. (ba)2b4a ⇒ (ab)3b3
  9. c(ba)3 ⇒ ba2bacb
  10. cb(ba)3 ⇒ b2a2bacb
  11. cb2(ba)3 ⇒ abab4ac
  12. a2(ba)2 ⇒ c
  13. cbab2(ba)3 ⇒ a2b2ab4ac
  14. cb2ab2(ba)3 ⇒ ba2b2ab4ac
  15. cb3ab2(ba)3 ⇒ b2a2b2ab4ac
  16. (ba)2b2(ba)3 ⇒ (ab)3(b4a)2c 
# ab:abababbbba=1 cb/a aababa=c frequency:6/4
bc=cb
cbbbb=1
cbabbbba=aab
cbbabbbba=baab
bbbaa=abbbbacbbb
cbbbabbbba=bbaab
cababa=aabacb
bababbbba=abababbbb
cbababa=baabacb
cbbababa=bbaabacb
cbbbababa=ababbbbac
aababa=c
cbabbbababa=aabbabbbbac
cbbabbbababa=baabbabbbbac
cbbbabbbababa=bbaabbabbbbac
bababbbababa=abababbbbbabbbbac

Right Cayley graph (truncated)

Left Cayley graph (truncated)