#159 ⟨a, b | abbabba=1⟩

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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. cd ⇒ 1
  2. dc ⇒ 1
  3. ac ⇒ ca
  4. ad ⇒ da
  5. a2 ⇒ c
  6. ab ⇒ dbca
  7. c2b ⇒ dbc3
  8. d2b ⇒ cbd3
  9. cb2 ⇒ b2c
  10. db2 ⇒ b2d
  11. b4 ⇒ d2a 
# ab:abbabba=1 cda/b aa=c,bbabb=d magic:0
cd=1
dc=1
ac=ca
ad=da
aa=c
ab=dbca
ccb=dbccc
ddb=cbddd
cbb=bbc
dbb=bbd
bbbb=dda

Right Cayley graph (truncated)

Left Cayley graph (truncated)