#718 ⟨a, b | ababbbaab=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. b3 ⇒ c
  6. a2b ⇒ bdaca
  7. acab2 ⇒ b2a2c
  8. a(ba)2c ⇒ (ba)2ca
  9. abacad ⇒ b2da(ba)2
  10. (ab)3c ⇒ (ba)2cab
  11. abacabd ⇒ b2d(ab)3
  12. (ab)3b ⇒ baca2
  13. abaca2 ⇒ b2d
  14. (aca)2d ⇒ b2ab2da(ba)2
  15. (aca)2bd ⇒ b2ab2d(ab)3
  16. a(ca2)2 ⇒ b2ab2d 
# ab:ababbbaab=1 reversed:cdb/a bbb=c,aababa=d magic:1
dc=1
cd=1
cb=bc
db=bd
bbb=c
aab=bdaca
acabb=bbaac
ababac=babaca
abacad=bbdababa
abababc=babacab
abacabd=bbdababab
abababb=bacaa
abacaa=bbd
acaacad=bbabbdababa
acaacabd=bbabbdababab
acaacaa=bbabbd

Right Cayley graph (truncated)

Left Cayley graph (truncated)