#1510 ⟨a, b | ababaabbba=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. b3 ⇒ c
  6. ba2ca ⇒ aca2b
  7. baba2 ⇒ ca2badb
  8. b2a2ba ⇒ aba2b2
  9. b2aca2 ⇒ ca2cadb2
  10. ca2(ba)2 ⇒ aca(ab)2
  11. daca2ba ⇒ a2(ba)2db2
  12. cba2(ba)2 ⇒ baca(ab)2
  13. dbaca2ba ⇒ ba2(ba)2db2
  14. a2ca2ba ⇒ db2
  15. b2a3ca2 ⇒ aba2b2acadb2
  16. (ca2ba)2 ⇒ aca2bab2a2b2
  17. d(aca2)2 ⇒ a2(ba)2db2acadb2
  18. cba2baca2ba ⇒ baca2bab2a2b2
  19. db(aca2)2 ⇒ ba2(ba)2db2acadb2
  20. a(aca2)2 ⇒ db2acadb2
  21. ca2b(aca2)2 ⇒ aca2b(ab2a)2cadb2
  22. cba2b(aca2)2 ⇒ baca2b(ab2a)2cadb2 
# ab:ababaabbba=1 cdb/a bbb=c,aababaa=d magic:1
cd=1
dc=1
bc=cb
bd=db
bbb=c
baaca=acaab
babaa=caabadb
bbaaba=abaabb
bbacaa=caacadbb
caababa=acaabab
dacaaba=aababadbb
cbaababa=bacaabab
dbacaaba=baababadbb
aacaaba=dbb
bbaaacaa=abaabbacadbb
caabacaaba=acaababbaabb
dacaaacaa=aababadbbacadbb
cbaabacaaba=bacaababbaabb
dbacaaacaa=baababadbbacadbb
aacaaacaa=dbbacadbb
caabacaaacaa=acaababbaabbacadbb
cbaabacaaacaa=bacaababbaabbacadbb

Right Cayley graph (truncated)

Left Cayley graph (truncated)