#10963 ⟨a, b | abab=aaa, bbbb=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. a19 ⇒ a7
  2. a17ba ⇒ a5ba
  3. a16ba2 ⇒ a4ba2
  4. aba3 ⇒ a4b
  5. (ab)2 ⇒ a3
  6. a16b2a ⇒ a4b2a
  7. (aba)2 ⇒ a6b2
  8. a4b2a2 ⇒ a14ba2b
  9. a3b3 ⇒ aba
  10. a4b2ab ⇒ a4ba2
  11. a4ba2b2a ⇒ a9ba2b2
  12. b4 ⇒ 1
  13. a4ba2b3 ⇒ a4b2a 
# ab:abab=aaa,bbbb=1 reversed:a/b
aaaaaaaaaaaaaaaaaaa=aaaaaaa
aaaaaaaaaaaaaaaaaba=aaaaaba
aaaaaaaaaaaaaaaabaa=aaaabaa
abaaa=aaaab
abab=aaa
aaaaaaaaaaaaaaaabba=aaaabba
abaaba=aaaaaabb
aaaabbaa=aaaaaaaaaaaaaabaab
aaabbb=aba
aaaabbab=aaaabaa
aaaabaabba=aaaaaaaaabaabb
bbbb=1
aaaabaabbb=aaaabba

Right Cayley graph (truncated)

Left Cayley graph (truncated)