#2352 ⟨a, b | abbabba=aab⟩

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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. a2b ⇒ c
  2. cb2a ⇒ ab2c
  3. a(b2a)2 ⇒ c
  4. (ab2)2c ⇒ cab
  5. ab2cab ⇒ cb2c
  6. c(ab)2 ⇒ a(b2c)2
  7. cab3a ⇒ cb2c
  8. cbab2a ⇒ ac
  9. cbab2c ⇒ acab
  10. cbcab ⇒ acb2c
  11. cb2cab ⇒ cab3c
  12. cab3cab ⇒ a(b2c)3 
# ab:abbabba=aab b/ac aab=c magic:0
aab=c
cbba=abbc
abbabba=c
abbabbc=cab
abbcab=cbbc
cabab=abbcbbc
cabbba=cbbc
cbabba=ac
cbabbc=acab
cbcab=acbbc
cbbcab=cabbbc
cabbbcab=abbcbbcbbc

Right Cayley graph (truncated)

Left Cayley graph (truncated)