#455 ⟨a, b | aabbaa=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. cb2 ⇒ c2bac
  3. acbac ⇒ cb
  4. c2ba2 ⇒ cb
  5. c2b(ac)2 ⇒ a(cb)2
  6. (cb)2ac ⇒ c2bacb
  7. acba2 ⇒ c
  8. c2baca2 ⇒ acbc
  9. (cb)2a2 ⇒ c2bac 
# ab:aabbaa=ab c/ab ab=c magic:0
ab=c
cbb=ccbac
acbac=cb
ccbaa=cb
ccbacac=acbcb
cbcbac=ccbacb
acbaa=c
ccbacaa=acbc
cbcbaa=ccbac

Right Cayley graph (truncated)

Left Cayley graph (truncated)