#1503 ⟨a, b | abaabbbaba=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. bc ⇒ cb
  2. b3 ⇒ c
  3. cd2b2d ⇒ dcd2b2
  4. bd2b2d ⇒ d3c
  5. bdcd2 ⇒ cd3b
  6. b2d3c ⇒ dcd2b2
  7. b2d3b ⇒ dcd2
  8. b(d2c)2 ⇒ cd3cdb
  9. bd2cd2b2 ⇒ cd3cd
  10. d(d2c)2 ⇒ b
  11. d3cd2b2 ⇒ 1
  12. cd3cd2 ⇒ b
  13. cd2bd3c ⇒ (d2c)2bd
  14. cd2cbd3c ⇒ dcd2cb2d2b2
  15. cd2cbd3b ⇒ dcd2cb2d2
  16. bd3cd2 ⇒ d3cd2b
  17. bd2bd3c ⇒ d3cdb2d
  18. bd2cbd3c ⇒ d3c2d2b2
  19. bd2cbd3b ⇒ d3c2d2
  20. b2d6c ⇒ dcd4b2d
  21. b2d4cd2 ⇒ dcd2bd3b
  22. cd5cd2b ⇒ (d2c)2bd3
  23. bd5cd2b ⇒ d3cdb2d3
  24. cd2cbd6c ⇒ dcd2cb2d4b2d
  25. cd2cbd4cd2 ⇒ dcd2cb2d2bd3b
  26. bd2cbd6c ⇒ d3c2d4b2d
  27. bd2cbd4cd2 ⇒ d3c2d2bd3b
  28. c(d5c)2 ⇒ (d2c)2bd5b2d
  29. b(d5c)2 ⇒ d3cdb2d5b2d
  30. a ⇒ b2d3 
# ab:abaabbbaba=1 cb/d/a bbb=c,aba=d frequency:3/4,3/0
bc=cb
bbb=c
cddbbd=dcddbb
bddbbd=dddc
bdcdd=cdddb
bbdddc=dcddbb
bbdddb=dcdd
bddcddc=cdddcdb
bddcddbb=cdddcd
dddcddc=b
dddcddbb=1
cdddcdd=b
cddbdddc=ddcddcbd
cddcbdddc=dcddcbbddbb
cddcbdddb=dcddcbbdd
bdddcdd=dddcddb
bddbdddc=dddcdbbd
bddcbdddc=dddccddbb
bddcbdddb=dddccdd
bbddddddc=dcddddbbd
bbddddcdd=dcddbdddb
cdddddcddb=ddcddcbddd
bdddddcddb=dddcdbbddd
cddcbddddddc=dcddcbbddddbbd
cddcbddddcdd=dcddcbbddbdddb
bddcbddddddc=dddccddddbbd
bddcbddddcdd=dddccddbdddb
cdddddcdddddc=ddcddcbdddddbbd
bdddddcdddddc=dddcdbbdddddbbd
a=bbddd

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
101538⟨a, b | abbabbaaab=1⟩φ(a) = d, φ(b) = bbddb