#2608 ⟨a, b | ababba=baab⟩

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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. ba2b ⇒ abac
  2. bcab ⇒ cbac
  3. b2a ⇒ c
  4. abacba ⇒ ba2c
  5. (cba)2 ⇒ bcac
  6. (ba)2c ⇒ cab
  7. ba3bac ⇒ abaca2b
  8. bca2bac ⇒ cbaca2b
  9. (abac)2 ⇒ ba2cab
  10. cbacabac ⇒ b(ca)2b
  11. ba2cbac ⇒ abac2ab
  12. bcacbac ⇒ cbac2ab
  13. baba2c ⇒ ab(ac)2ba
  14. bcba2c ⇒ cb(ac)2ba
  15. (ab)2cac ⇒ ba2c2ba
  16. cbabcac ⇒ bcac2ba 
# ab:ababba=baab reversed:ac/b bba=c frequency:3/0
baab=abac
bcab=cbac
bba=c
abacba=baac
cbacba=bcac
babac=cab
baaabac=abacaab
bcaabac=cbacaab
abacabac=baacab
cbacabac=bcacab
baacbac=abaccab
bcacbac=cbaccab
babaac=abacacba
bcbaac=cbacacba
ababcac=baaccba
cbabcac=bcaccba

Right Cayley graph (truncated)

Left Cayley graph (truncated)