#2609 ⟨a, b | ababba=baba⟩

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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. ca2c2 ⇒ ac2ac
  2. acac2 ⇒ cac
  3. c(ac)2bc ⇒ ac4
  4. ac2acbc ⇒ c3
  5. a2c2bc ⇒ c2
  6. bc2 ⇒ a2c3bc
  7. cba ⇒ ac2
  8. bcac ⇒ a2c2ac3
  9. bac2 ⇒ (ac)2bc
  10. ba2c ⇒ a2c2
  11. b(ac)2 ⇒ a(ac2)2
  12. ba3c2 ⇒ (ac)2
  13. (ab)2c ⇒ bac
  14. cb2a ⇒ babc
  15. (ba)2 ⇒ ac
  16. b2ac ⇒ acbc
  17. bab2a ⇒ c 
# ab:ababba=baba reversed:c/a/b babba=c frequency:5/2
caacc=accac
acacc=cac
cacacbc=acccc
accacbc=ccc
aaccbc=cc
bcc=aacccbc
cba=acc
bcac=aaccaccc
bacc=acacbc
baac=aacc
bacac=aaccacc
baaacc=acac
ababc=bac
cbba=babc
baba=ac
bbac=acbc
babba=c

Right Cayley graph (truncated)

Left Cayley graph (truncated)