#1916 ⟨a, b | aaabbaba=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. ab ⇒ c
  2. a2cbca ⇒ c
  3. a2cbc2 ⇒ cb
  4. cacbca ⇒ cb
  5. cb2 ⇒ cacbc2
  6. cbacbca ⇒ cacbc2
  7. a2(cb)2 ⇒ c2bca
  8. ca(cb)2 ⇒ c(bc)2a
  9. cacbc2b ⇒ cbacbc2
  10. cba(cb)2 ⇒ cacbc3bca
  11. cbacbc2b ⇒ c(acbc2)2 
# ab:aaabbaba=ab ac/b ab=c magic:0
ab=c
aacbca=c
aacbcc=cb
cacbca=cb
cbb=cacbcc
cbacbca=cacbcc
aacbcb=ccbca
cacbcb=cbcbca
cacbccb=cbacbcc
cbacbcb=cacbcccbca
cbacbccb=cacbccacbcc

Right Cayley graph (truncated)

Left Cayley graph (truncated)