#2286 ⟨a, b | aabbbba=abb⟩

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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. cb2 ⇒ cabc
  2. ab2 ⇒ a2bc
  3. c(bc)2a ⇒ ca(bc)2
  4. a(bc)2a ⇒ a2(bc)2
  5. cabcba ⇒ c2
  6. b3a ⇒ c
  7. (cb)3a ⇒ (cab)2c2
  8. a2bcba ⇒ ac
  9. ca(bca)2 ⇒ cbc
  10. ab(cb)2a ⇒ a(abc)2c
  11. a2(bca)2 ⇒ abc 
# ab:aabbbba=abb c/ab bbba=c frequency:4/0
cbb=cabc
abb=aabc
cbcbca=cabcbc
abcbca=aabcbc
cabcba=cc
bbba=c
cbcbcba=cabcabcc
aabcba=ac
cabcabca=cbc
abcbcba=aabcabcc
aabcabca=abc

Right Cayley graph (truncated)

Left Cayley graph (truncated)