#1375 ⟨a, b | aaabbabbaa=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. da5 ⇒ 1
  2. ad ⇒ da
  3. a4c ⇒ ca4
  4. dc ⇒ a3cd2a2
  5. dac ⇒ cda
  6. da2c ⇒ acda
  7. da3c ⇒ a2cda
  8. cac ⇒ d
  9. bc ⇒ cb
  10. bac ⇒ aca5bd
  11. b2 ⇒ c 
# ab:aaabbabbaa=1 a/d/cb bb=c,cac=d frequency:2/1,3/2
daaaaa=1
ad=da
aaaac=caaaa
dc=aaacddaa
dac=cda
daac=acda
daaac=aacda
cac=d
bc=cb
bac=acaaaaabd
bb=c

Right Cayley graph (truncated)

Left Cayley graph (truncated)

Other anti-isomorphic instances

The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.

1 total

Σ#PresentationMapping
101504⟨a, b | abaabbbbba=1⟩φ(a) = b, φ(b) = a