#575 ⟨a, b | abba=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. cba ⇒ abc
  2. cab ⇒ abc
  3. c2b ⇒ cbc
  4. c2a ⇒ cac
  5. (ab)2 ⇒ ab2a
  6. abcb ⇒ ab2c
  7. cbca ⇒ abc2
  8. ca2b ⇒ abca
  9. cacb ⇒ abc2
  10. ab2ab ⇒ c
  11. ab2ca ⇒ ab2ac
  12. ab2a2b ⇒ ca
  13. ab2acb ⇒ c2 
# ab:abba=abab bac abbab=c frequency:5/0
cba=abc
cab=abc
ccb=cbc
cca=cac
abab=abba
abcb=abbc
cbca=abcc
caab=abca
cacb=abcc
abbab=c
abbca=abbac
abbaab=ca
abbacb=cc

Right Cayley graph (truncated)

Left Cayley graph (truncated)