#2611 ⟨a, b | ababba=bbaa⟩

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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. abac ⇒ ca
  2. b2a2 ⇒ c
  3. b2aca ⇒ cbac
  4. abab2a ⇒ c
  5. abab2c ⇒ b2ac
  6. cbab2a ⇒ b2ac
  7. (b2a)2c ⇒ cbab2c
  8. cbab2ca ⇒ b(bac)2
  9. c(bac)2 ⇒ b2ac2a
  10. abab4ac ⇒ cbab2c
  11. cbab4ac ⇒ b2acbab2c
  12. (cba)2b2c ⇒ (b2ac)2 
# ab:ababba=bbaa abc bbaa=c magic:0
abac=ca
bbaa=c
bbaca=cbac
ababba=c
ababbc=bbac
cbabba=bbac
bbabbac=cbabbc
cbabbca=bbacbac
cbacbac=bbacca
ababbbbac=cbabbc
cbabbbbac=bbacbabbc
cbacbabbc=bbacbbac

Right Cayley graph (truncated)

Left Cayley graph (truncated)