#1666 ⟨a, b | aabaaaaba=b⟩

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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. (a2b)2 ⇒ ba3ba
  2. a2ba4ba ⇒ b
  3. b(a3b)2 ⇒ a2b2a3ba
  4. a2ba4b2 ⇒ baba4ba
  5. ba5b2ab ⇒ a2b2(aba)2
  6. a2ba6b2 ⇒ ba2ba5ba
  7. ba3ba5ba ⇒ a2b2
  8. ba3ba5b2 ⇒ a2b2aba4ba
  9. a2b2a3ba4b ⇒ ba5b2a3ba
  10. ba2(a3b2)2 ⇒ a(ab2)2a4ba
  11. ba5b2a3ba2 ⇒ a2b2ab
  12. ba5b2a3bab ⇒ a2b(ba)3a3ba
  13. ba3ba7b2 ⇒ a2b2a2ba5ba
  14. b(a5b2)2 ⇒ a2b(ba)3a4ba
  15. a2b2a3ba6ba ⇒ ba5b2
  16. (ba3ba)2a3b ⇒ (a2b2a3)2ba
  17. a2b2a3ba8b2 ⇒ ba5b2a2ba5ba
  18. (ba3ba)2a5ba ⇒ a2b2a5b2
  19. (ba3ba)2a7b2 ⇒ a2b2a5b2a2ba5ba 
# ab:aabaaaaba=b reversed:ab
aabaab=baaaba
aabaaaaba=b
baaabaaab=aabbaaaba
aabaaaabb=babaaaaba
baaaaabbab=aabbabaaba
aabaaaaaabb=baabaaaaaba
baaabaaaaaba=aabb
baaabaaaaabb=aabbabaaaaba
aabbaaabaaaab=baaaaabbaaaba
baaaaabbaaabb=aabbabbaaaaba
baaaaabbaaabaa=aabbab
baaaaabbaaabab=aabbababaaaaba
baaabaaaaaaabb=aabbaabaaaaaba
baaaaabbaaaaabb=aabbababaaaaaba
aabbaaabaaaaaaba=baaaaabb
baaababaaabaaaab=aabbaaaaabbaaaba
aabbaaabaaaaaaaabb=baaaaabbaabaaaaaba
baaababaaabaaaaaaba=aabbaaaaabb
baaababaaabaaaaaaaabb=aabbaaaaabbaabaaaaaba

Right Cayley graph (truncated)

Left Cayley graph (truncated)