#22287 ⟨a, b | aaa=1, abbbba=bb⟩

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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. c4 ⇒ c
  2. cac3 ⇒ ca
  3. c3a ⇒ ac3
  4. ac2a ⇒ c2ac2
  5. ca2c3 ⇒ ca2
  6. (ca)2 ⇒ (ac)2
  7. a3 ⇒ 1
  8. a2ca ⇒ c2a2c
  9. aca2 ⇒ ca2c2
  10. cbc3 ⇒ cb
  11. cbac3 ⇒ cba
  12. cba2c3 ⇒ cba2
  13. c3b ⇒ bc3
  14. abc ⇒ cbc2ac
  15. abac ⇒ cbc2a2c
  16. aba2c ⇒ cb
  17. ac2b ⇒ c2bcac2
  18. cab ⇒ c2bc2a
  19. cacb ⇒ acbca2c2
  20. a2cb ⇒ ba2c
  21. ca2b ⇒ acba2c
  22. b2 ⇒ a2c
  23. cbab ⇒ (cb)2c2a
  24. cba2b ⇒ cbacbc2a 
# ab:aaa=1,abbbba=bb c/a/b abb=c frequency:3/0
cccc=c
caccc=ca
ccca=accc
acca=ccacc
caaccc=caa
caca=acac
aaa=1
aaca=ccaac
acaa=caacc
cbccc=cb
cbaccc=cba
cbaaccc=cbaa
cccb=bccc
abc=cbccac
abac=cbccaac
abaac=cb
accb=ccbcacc
cab=ccbcca
cacb=acbcaacc
aacb=baac
caab=acbaac
bb=aac
cbab=cbcbcca
cbaab=cbacbcca

Right Cayley graph (truncated)

Left Cayley graph (truncated)