#2523 ⟨a, b | aabbaa=aaba⟩

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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. a2ba ⇒ c
  2. caba ⇒ a2bc
  3. cb2a2 ⇒ cba
  4. cb2ac ⇒ cbc
  5. c(ba)2 ⇒ cb2c
  6. a2b2c ⇒ cba
  7. a2b2a2 ⇒ c
  8. a2b2ac ⇒ a2bc
  9. cab2c ⇒ a2bcba
  10. cab2a2 ⇒ a2bc
  11. cab2ac ⇒ cabc
  12. cbab2c ⇒ cb2cba
  13. cbab2a2 ⇒ cb2c
  14. cbab2ac ⇒ cbabc 
# ab:aabbaa=aaba ac/b aaba=c magic:0
aaba=c
caba=aabc
cbbaa=cba
cbbac=cbc
cbaba=cbbc
aabbc=cba
aabbaa=c
aabbac=aabc
cabbc=aabcba
cabbaa=aabc
cabbac=cabc
cbabbc=cbbcba
cbabbaa=cbbc
cbabbac=cbabc

Right Cayley graph (truncated)

Left Cayley graph (truncated)