#706 ⟨a, b | abaababba=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. cb ⇒ bc
  2. b2 ⇒ c
  3. dbd2c ⇒ bd2cd
  4. cd3b ⇒ bd2cd
  5. bd3b ⇒ d2cd
  6. dbd2b ⇒ cd3
  7. d2cdb ⇒ bd3c
  8. (cd2)2b ⇒ bdcd3c
  9. bd2cd2b ⇒ dcd3c
  10. cd2cd3 ⇒ b
  11. bd2cd3 ⇒ 1
  12. cd5c ⇒ d(cd2)2
  13. d2cd3c ⇒ b
  14. cd(d2c)2 ⇒ bd2bcd2cd
  15. bd(d2c)2 ⇒ d2bcd2cd
  16. cd5b ⇒ dbdcd3
  17. cd3cd2b ⇒ bd2c2d3
  18. bd3cd2b ⇒ d2c2d3
  19. cd6b ⇒ dbd4cd
  20. d2cd4b ⇒ bd5cd
  21. cd6cd2c ⇒ dbd4bcd2cd
  22. (d2cd2)2c ⇒ bd5bcd2cd
  23. cd6cd2b ⇒ dbd4c2d3
  24. (d2cd2)2b ⇒ bd5c2d3
  25. a ⇒ dbd2 
# ab:abaababba=1 reversed:cb/d/a bb=c,aab=d frequency:2/3,3/1
cb=bc
bb=c
dbddc=bddcd
cdddb=bddcd
bdddb=ddcd
dbddb=cddd
ddcdb=bdddc
cddcddb=bdcdddc
bddcddb=dcdddc
cddcddd=b
bddcddd=1
cdddddc=dcddcdd
ddcdddc=b
cdddcddc=bddbcddcd
bdddcddc=ddbcddcd
cdddddb=dbdcddd
cdddcddb=bddccddd
bdddcddb=ddccddd
cddddddb=dbddddcd
ddcddddb=bdddddcd
cddddddcddc=dbddddbcddcd
ddcddddcddc=bdddddbcddcd
cddddddcddb=dbddddccddd
ddcddddcddb=bdddddccddd
a=dbdd

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
9723⟨a, b | abbaabaab=1⟩φ(a) = dbdd, φ(b) = b

Other anti-isomorphic instances

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

1 total

Σ#PresentationMapping
9708⟨a, b | abaabbaba=1⟩φ(a) = bddd, φ(b) = b