#728 ⟨a, b | abbbaaaab=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. cd ⇒ 1
  2. dc ⇒ 1
  3. ac ⇒ ca
  4. ad ⇒ da
  5. a4 ⇒ c
  6. cbab ⇒ bcba
  7. dbcb ⇒ babda3
  8. c(ab)2 ⇒ abcba
  9. dabcb ⇒ (ab)2da3
  10. ca(ab)2 ⇒ a2bcba
  11. da2bcb ⇒ a(ab)2da3
  12. ca3bab ⇒ a3bcba
  13. da3bcb ⇒ a3babda3
  14. db2cb ⇒ bab2da3
  15. ab3 ⇒ b2cbda
  16. dab2cb ⇒ abab2da3
  17. da2b2cb ⇒ a2bab2da3
  18. a3b2cb ⇒ cb3a3
  19. a3bab2 ⇒ b3c
  20. b3cb ⇒ da3 
# ab:abbbaaaab=1 cda/b aaaa=c,babbb=d magic:0
cd=1
dc=1
ac=ca
ad=da
aaaa=c
cbab=bcba
dbcb=babdaaa
cabab=abcba
dabcb=ababdaaa
caabab=aabcba
daabcb=aababdaaa
caaabab=aaabcba
daaabcb=aaababdaaa
dbbcb=babbdaaa
abbb=bbcbda
dabbcb=ababbdaaa
daabbcb=aababbdaaa
aaabbcb=cbbbaaa
aaababb=bbbc
bbbcb=daaa

Right Cayley graph (truncated)

Left Cayley graph (truncated)