#2005 ⟨a, b | aabbbaba=ab⟩

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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. ab2 ⇒ c
  2. cb3 ⇒ c2babc
  3. acbabc ⇒ cb
  4. c2(ba)2 ⇒ cb
  5. cb2abc ⇒ acbcb2
  6. (cb)2abc ⇒ c2babcb
  7. ac(ba)2 ⇒ ab
  8. abcbabc ⇒ cb2
  9. c2b(abc)2 ⇒ a(bc)2b2
  10. cb(ba)2 ⇒ acbc
  11. cbc(ba)2 ⇒ cb2
  12. cb2cbabc ⇒ c2babcb2
  13. abc(ba)2 ⇒ c
  14. c2babcaba ⇒ a(bc)2
  15. cb2c(ba)2 ⇒ c2babc 
# ab:aabbbaba=ab c/ab abb=c frequency:3/1
abb=c
cbbb=ccbabc
acbabc=cb
ccbaba=cb
cbbabc=acbcbb
cbcbabc=ccbabcb
acbaba=ab
abcbabc=cbb
ccbabcabc=abcbcbb
cbbaba=acbc
cbcbaba=cbb
cbbcbabc=ccbabcbb
abcbaba=c
ccbabcaba=abcbc
cbbcbaba=ccbabc

Right Cayley graph (truncated)

Left Cayley graph (truncated)