#1451 ⟨a, b | aabbababba=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. da ⇒ ad
  4. ca ⇒ ac
  5. a3 ⇒ c
  6. bcb2a ⇒ ab2cb
  7. b(ba)2 ⇒ adbab2c
  8. bab2a2 ⇒ a2b2ab
  9. b2cba2 ⇒ a2dbcb2c
  10. bab2cbd ⇒ a2d(ba)2b2
  11. (ba)2b2c ⇒ abab2cb
  12. bab2cbad ⇒ a2d(ba)2b2a
  13. (ba)2b2ac ⇒ abab2cba
  14. bab2cb2 ⇒ a2d
  15. b2cb3a2 ⇒ a2dbcba2b2ab
  16. (b2cb)2d ⇒ a2dbcba2d(ba)2b2
  17. (bab2c)2 ⇒ a2b2a2bab2cb
  18. (b2cb)2ad ⇒ a2dbcba2d(ba)2b2a
  19. bab2cbab2ac ⇒ a2b2a2bab2cba
  20. b(bcb2)2 ⇒ a2dbcba2d
  21. (b2cb)2ab2c ⇒ a2dbc(ba2b)2ab2cb
  22. (b2cb)2ab2ac ⇒ a2dbc(ba2b)2ab2cba 
# ab:aabbababba=1 reversed:dca/b aaa=c,bbababb=d magic:0
cd=1
dc=1
da=ad
ca=ac
aaa=c
bcbba=abbcb
bbaba=adbabbc
babbaa=aabbab
bbcbaa=aadbcbbc
babbcbd=aadbababb
bababbc=ababbcb
babbcbad=aadbababba
bababbac=ababbcba
babbcbb=aad
bbcbbbaa=aadbcbaabbab
bbcbbbcbd=aadbcbaadbababb
babbcbabbc=aabbaababbcb
bbcbbbcbad=aadbcbaadbababba
babbcbabbac=aabbaababbcba
bbcbbbcbb=aadbcbaad
bbcbbbcbabbc=aadbcbaabbaababbcb
bbcbbbcbabbac=aadbcbaabbaababbcba

Right Cayley graph (truncated)

Left Cayley graph (truncated)