#2633 ⟨a, b | abbbba=babb⟩

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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. bab2 ⇒ cba
  2. ab3 ⇒ c
  3. cbab ⇒ bc
  4. c2ba ⇒ bcb
  5. ab2cba ⇒ cab2
  6. bcb2 ⇒ cbc
  7. cba2b2 ⇒ babcba
  8. (cba)2 ⇒ bcab2
  9. ab(bc)2 ⇒ c2b2
  10. cbcab2 ⇒ b(cb)2a
  11. cbacb2 ⇒ ba(bc)2
  12. cbacbc ⇒ bc2b2
  13. cbc2b2 ⇒ (bc)3
  14. c2b4 ⇒ ab2c2bc
  15. c2b3ab ⇒ abcbc2
  16. c2b2cba ⇒ abcbc2b
  17. c2b3a2b2 ⇒ a(bc)2abcba
  18. c2b3acba ⇒ abcbc2ab2
  19. c2b3cab2 ⇒ ab(cbc)2ba
  20. c2b3acb2 ⇒ (a(bc)2)2
  21. c2b3acbc ⇒ abcbc3b2
  22. c2b3c2b2 ⇒ ab(cbc)2bc 
# ab:abbbba=babb a/bc abbb=c frequency:4/1
babb=cba
abbb=c
cbab=bc
ccba=bcb
abbcba=cabb
bcbb=cbc
cbaabb=babcba
cbacba=bcabb
abbcbc=ccbb
cbcabb=bcbcba
cbacbb=babcbc
cbacbc=bccbb
cbccbb=bcbcbc
ccbbbb=abbccbc
ccbbbab=abcbcc
ccbbcba=abcbccb
ccbbbaabb=abcbcabcba
ccbbbacba=abcbccabb
ccbbbcabb=abcbccbcba
ccbbbacbb=abcbcabcbc
ccbbbacbc=abcbcccbb
ccbbbccbb=abcbccbcbc

Right Cayley graph (truncated)

Left Cayley graph (truncated)