#1443 ⟨a, b | aabbaababa=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. ad ⇒ da
  2. da3 ⇒ 1
  3. ba3c ⇒ da2
  4. cab ⇒ d
  5. b2 ⇒ ca3cda2
  6. bab ⇒ aca4cda
  7. ba2b ⇒ a3cac
  8. ba3b ⇒ (a2c)2a
  9. ca4cac ⇒ da2b
  10. ca(a2c)2 ⇒ bda2
  11. caca3c ⇒ dba
  12. ca2ca4c ⇒ daba2
  13. cacb ⇒ dba2ca3cda2
  14. ca3cb ⇒ baca4cda
  15. ca4cb ⇒ da2ba4cac
  16. caca2b ⇒ dba5cac
  17. (ca2)2b ⇒ dab(a4c)2da
  18. ca3ca2b ⇒ b(a2c)2a
  19. ca4cdab ⇒ da2baca3cda2
  20. caca3b ⇒ dba3(aca)2
  21. ca2ca3b ⇒ daba6cac
  22. ca3cda2b ⇒ bca3cda2
  23. ca4cda2b ⇒ da2ba2ca4cda
  24. ca2ca4b ⇒ daba4(aca)2 
# ab:aabbaababa=1 reversed:ad/cb bbaab=c,cab=d frequency:5/0,3/0
ad=da
daaa=1
baaac=daa
cab=d
bb=caaacdaa
bab=acaaaacda
baab=aaacac
baaab=aacaaca
caaaacac=daab
caaacaac=bdaa
cacaaac=dba
caacaaaac=dabaa
cacb=dbaacaaacdaa
caaacb=bacaaaacda
caaaacb=daabaaaacac
cacaab=dbaaaaacac
caacaab=dabaaaacaaaacda
caaacaab=baacaaca
caaaacdab=daabacaaacdaa
cacaaab=dbaaaacaaca
caacaaab=dabaaaaaacac
caaacdaab=bcaaacdaa
caaaacdaab=daabaacaaaacda
caacaaaab=dabaaaaacaaca

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
101498⟨a, b | abaabbaaab=1⟩φ(a) = a, φ(b) = b