#1453 ⟨a, b | aabbabbaba=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. dc ⇒ 1
  2. cd ⇒ 1
  3. cb ⇒ bc
  4. db ⇒ bd
  5. b2 ⇒ c
  6. a3c ⇒ baba2
  7. aba2d ⇒ bda3
  8. a(ca)2b ⇒ (ca)2ba
  9. ac(ab)2 ⇒ d(ac)3
  10. a3bc ⇒ baba2b
  11. aba2bd ⇒ bda3b
  12. aba3b ⇒ da2(ca)2
  13. acaba2b ⇒ da(ac)3
  14. acaba3 ⇒ d
  15. (ac)3a2d ⇒ caca4
  16. a(ac)2a2b ⇒ ba2d(ac)3
  17. (ac)3a2bd ⇒ caca4b
  18. a(ac)2a3d ⇒ (ba3)2
  19. a(ac)2a3b ⇒ ba2da(ac)3
  20. (ac)3a3b ⇒ (ca)2bda2(ca)2
  21. a2da(ac)3c ⇒ bda2(cab)2a2b
  22. a(ac)2a4 ⇒ ba2d 
# ab:aabbabbaba=1 reversed:cdb/a bb=c,abbabaaa=d magic:1
dc=1
cd=1
cb=bc
db=bd
bb=c
aaac=babaa
abaad=bdaaa
acacab=cacaba
acabab=dacacac
aaabc=babaab
abaabd=bdaaab
abaaab=daacaca
acabaab=daacacac
acabaaa=d
acacacaad=cacaaaa
aacacaab=baadacacac
acacacaabd=cacaaaab
aacacaaad=baaabaaa
aacacaaab=baadaacacac
acacacaaab=cacabdaacaca
aadaacacacc=bdaacabcabaab
aacacaaaa=baad

Right Cayley graph (truncated)

Left Cayley graph (truncated)