#1457 ⟨a, b | aabbbaaaab=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 ⇒ 1
  2. cb ⇒ 1
  3. ba2b3a ⇒ aba2b3
  4. caba2 ⇒ a2b3ac3
  5. ca2ba2 ⇒ a2b3a2c3
  6. ca2b3a2 ⇒ ba4b
  7. b2a4 ⇒ a2b3a2c
  8. ba2b2aba2 ⇒ a2ba2b6ac3
  9. ca3ba2 ⇒ a2b3a3c3
  10. ca2b2aba2 ⇒ ba4b4ac3
  11. a4ba2 ⇒ c3
  12. (ba2b)2a2 ⇒ a2ba2b6a2c3
  13. ca2b(ba2)2 ⇒ ba4b4a2c3
  14. ba2b2a3ba2 ⇒ a2ba2b6a3c3
  15. ca2b2a3ba2 ⇒ ba4b4a3c3 
# ab:aabbbaaaab=1 bc/a aabbbaaaa=c frequency:9/3
bc=1
cb=1
baabbba=abaabbb
cabaa=aabbbaccc
caabaa=aabbbaaccc
caabbbaa=baaaab
bbaaaa=aabbbaac
baabbabaa=aabaabbbbbbaccc
caaabaa=aabbbaaaccc
caabbabaa=baaaabbbbaccc
aaaabaa=ccc
baabbaabaa=aabaabbbbbbaaccc
caabbaabaa=baaaabbbbaaccc
baabbaaabaa=aabaabbbbbbaaaccc
caabbaaabaa=baaaabbbbaaaccc

Right Cayley graph (truncated)

Left Cayley graph (truncated)