#1447 ⟨a, b | aabbabaaab=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. dc ⇒ cd
  2. bc ⇒ cb
  3. b2 ⇒ c
  4. cd2 ⇒ 1
  5. bd2 ⇒ d2b
  6. dacda ⇒ abad2b
  7. ba2 ⇒ acdabd
  8. bacda ⇒ ca2db
  9. cdaba ⇒ acdab
  10. bdaba ⇒ a2cd
  11. a2cda ⇒ d2b
  12. dacaba ⇒ (ab)2dab
  13. bacaba ⇒ ca2cdbdab
  14. cdaca2 ⇒ acdacbdabd
  15. bdaca2 ⇒ a2cabd
  16. a2caba ⇒ bdab
  17. d(ac)2a2 ⇒ (ab)2dacbdabd
  18. b(ac)2a2 ⇒ ca2cdbdacbdabd
  19. a(ac)2a2 ⇒ bdacbdabd 
# ab:aabbabaaab=1 cdb/a bb=c,abaa=d frequency:2/3,4/3
dc=cd
bc=cb
bb=c
cdd=1
bdd=ddb
dacda=abaddb
baa=acdabd
bacda=caadb
cdaba=acdab
bdaba=aacd
aacda=ddb
dacaba=ababdab
bacaba=caacdbdab
cdacaa=acdacbdabd
bdacaa=aacabd
aacaba=bdab
dacacaa=ababdacbdabd
bacacaa=caacdbdacbdabd
aacacaa=bdacbdabd

Right Cayley graph (truncated)

Left Cayley graph (truncated)

Other isomorphic instances

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

1 total

Σ#PresentationMapping
101523⟨a, b | ababbbabba=1⟩φ(a) = b, φ(b) = a