#2552 ⟨a, b | aabbba=abab⟩

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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. (ab)2 ⇒ c
  2. cab ⇒ abc
  3. a2b3a ⇒ c
  4. a2b3c ⇒ cbab
  5. abcb2a ⇒ cbab
  6. c2b2a ⇒ abcbab
  7. c(bab)2 ⇒ abcb2c
  8. cbcb2a ⇒ abcb2c
  9. a(bcb)2ab ⇒ cbcb2c
  10. cbab2cb2a ⇒ cbcb2c
  11. c2b2cbab ⇒ a(bc)2b2c
  12. c(bcb)2ab ⇒ cba(b2c)2
  13. cba(b2c)2bab ⇒ a(bcb2c)2 
# ab:aabbba=abab a/bc abab=c magic:0
abab=c
cab=abc
aabbba=c
aabbbc=cbab
abcbba=cbab
ccbba=abcbab
cbabbab=abcbbc
cbcbba=abcbbc
abcbbcbab=cbcbbc
cbabbcbba=cbcbbc
ccbbcbab=abcbcbbc
cbcbbcbab=cbabbcbbc
cbabbcbbcbab=abcbbcbcbbc

Right Cayley graph (truncated)

Left Cayley graph (truncated)