#1392 ⟨a, b | aabaaaaaba=1⟩

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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. c2b ⇒ bc2
  2. c2a ⇒ ac2
  3. (cb)2 ⇒ (bc)2
  4. bca ⇒ c2
  5. ab ⇒ c
  6. acb ⇒ bac
  7. ca2 ⇒ a2c
  8. cb2cb ⇒ bcb2c
  9. bcba ⇒ cbc
  10. ba2 ⇒ ac
  11. a3c6 ⇒ b2cb
  12. a2cac5 ⇒ bcb2
  13. (ac)3c2 ⇒ b3
  14. b3cb ⇒ acac6
  15. b2cb2 ⇒ a2c7
  16. bcb3 ⇒ (ca)2c5
  17. bcb2a ⇒ cb2c
  18. a4c5 ⇒ bcb
  19. a3cac3 ⇒ b2
  20. (ac)4c ⇒ b3a
  21. a5c3 ⇒ b
  22. a2(ac)3c ⇒ b2a
  23. a6c2 ⇒ 1
  24. a5cac2 ⇒ ba 
# ab:aabaaaaaba=1 c/ba ab=c frequency:2/1
ccb=bcc
cca=acc
cbcb=bcbc
bca=cc
ab=c
acb=bac
caa=aac
cbbcb=bcbbc
bcba=cbc
baa=ac
aaacccccc=bbcb
aacaccccc=bcbb
acacaccc=bbb
bbbcb=acacccccc
bbcbb=aaccccccc
bcbbb=cacaccccc
bcbba=cbbc
aaaaccccc=bcb
aaacaccc=bb
acacacacc=bbba
aaaaaccc=b
aaacacacc=bba
aaaaaacc=1
aaaaacacc=ba

Right Cayley graph (truncated)

Left Cayley graph (truncated)