#1490 ⟨a, b | abaaabbbba=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. bc ⇒ cb
  4. bd ⇒ db
  5. b4 ⇒ c
  6. ca2ba ⇒ aca2b
  7. daca2 ⇒ a2badb3
  8. ba3 ⇒ aca2db
  9. cba2ba ⇒ baca2b
  10. dbaca2 ⇒ ba2badb3
  11. cb2a2ba ⇒ b2aca2b
  12. db2aca2 ⇒ b2a2badb3
  13. b3a2ba ⇒ a3c
  14. b3aca2 ⇒ ca3b3
  15. da2ca2 ⇒ a2ba2db3
  16. dba2ca2 ⇒ (ba2)2db3
  17. db2a2ca2 ⇒ b(ba2)2db3
  18. b3a2ca2 ⇒ ca3cadb3
  19. a3ca2 ⇒ db3 
# ab:abaaabbbba=1 cdb/a bbbb=c,aabaaa=d magic:1
cd=1
dc=1
bc=cb
bd=db
bbbb=c
caaba=acaab
dacaa=aabadbbb
baaa=acaadb
cbaaba=bacaab
dbacaa=baabadbbb
cbbaaba=bbacaab
dbbacaa=bbaabadbbb
bbbaaba=aaac
bbbacaa=caaabbb
daacaa=aabaadbbb
dbaacaa=baabaadbbb
dbbaacaa=bbaabaadbbb
bbbaacaa=caaacadbbb
aaacaa=dbbb

Right Cayley graph (truncated)

Left Cayley graph (truncated)