#22800 ⟨a, b | aaa=1, ababb=bba⟩

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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. abab2 ⇒ b2a
  2. a3 ⇒ 1
  3. bab2a2 ⇒ a2b2
  4. a2b2a ⇒ bab2
  5. a2b4a ⇒ (bab2)2
  6. a2b3ab2 ⇒ ba(b2a)2
  7. (bab2)3 ⇒ a2b6a
  8. bab(b2a)3 ⇒ a2b5ab2
  9. (a2b)2b ⇒ bab4a2
  10. (ab)2a2b2 ⇒ b(b2a)2
  11. bab3aba2b2 ⇒ a2b5ab2a
  12. a2b3a2b2 ⇒ bab3ab4a2
  13. a2b4(bab2)2 ⇒ (bab2)2ab4a
  14. a2b3(b2a)3 ⇒ b(ab3ab2)2
  15. (bab2)2aba2b2 ⇒ a2b5ab4a2
  16. a2b3aba2b2 ⇒ (bab)2(b2a)2
  17. a2b5aba2b2 ⇒ ba(b(b2a)2)2
  18. a2b4(bab)2a2b2 ⇒ (bab3ab)2b3a2 
# ab:aaa=1,ababb=bba reversed:b/a
ababb=bba
aaa=1
babbaa=aabb
aabba=babb
aabbbba=babbbabb
aabbbabb=babbabba
babbbabbbabb=aabbbbbba
babbbabbabba=aabbbbbabb
aabaabb=babbbbaa
ababaabb=bbbabba
babbbabaabb=aabbbbbabba
aabbbaabb=babbbabbbbaa
aabbbbbabbbabb=babbbabbabbbba
aabbbbbabbabba=babbbabbabbbabb
babbbabbabaabb=aabbbbbabbbbaa
aabbbabaabb=babbabbbabba
aabbbbbabaabb=babbbabbabbbabba
aabbbbbabbabaabb=babbbabbabbbabbbbaa

Right Cayley graph (truncated)

Left Cayley graph (truncated)