#2525 ⟨a, b | aabbaa=abab⟩

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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. (ab)2 ⇒ c
  2. a2b2a2 ⇒ c
  3. cab ⇒ abc
  4. abcba2 ⇒ a2b2ac
  5. cb2a2 ⇒ a2b2c
  6. cbab ⇒ a2b2ac
  7. aba2b2ac ⇒ c2ba2
  8. ca2b2ac ⇒ abc2ba2
  9. (cb)2a2 ⇒ abcbac
  10. c2ba3b ⇒ a(bc)2
  11. cba2b2ac ⇒ a2b2ac2ba2
  12. a2(b2ac)2 ⇒ c(cba2)2
  13. c2ba4b2ac ⇒ abcbc2ba2
  14. c(cba2)2ab ⇒ a(bc)3
  15. abcbacb2ac ⇒ a2b2ac(cba2)2
  16. c(b2ac)2 ⇒ a2b2c(cba2)2
  17. c(cba2)3 ⇒ c2bacb2ac
  18. (cb)2acb2ac ⇒ abcbac(cba2)2
  19. c(cba2)2a2b2ac ⇒ a(bc)3cba2
  20. c2ba(acb)2bac ⇒ c2bacb2ac2ba2
  21. c2b(a2cb)2acb2ac ⇒ c2bacb2ac(cba2)2 
# ab:aabbaa=abab a/bc abab=c magic:0
abab=c
aabbaa=c
cab=abc
abcbaa=aabbac
cbbaa=aabbc
cbab=aabbac
abaabbac=ccbaa
caabbac=abccbaa
cbcbaa=abcbac
ccbaaab=abcbc
cbaabbac=aabbaccbaa
aabbacbbac=ccbaacbaa
ccbaaaabbac=abcbccbaa
ccbaacbaaab=abcbcbc
abcbacbbac=aabbaccbaacbaa
cbbacbbac=aabbccbaacbaa
ccbaacbaacbaa=ccbacbbac
cbcbacbbac=abcbaccbaacbaa
ccbaacbaaaabbac=abcbcbccbaa
ccbaacbacbbac=ccbacbbaccbaa
ccbaacbaacbacbbac=ccbacbbaccbaacbaa

Right Cayley graph (truncated)

Left Cayley graph (truncated)