#1125 ⟨a, b | ababba=baa⟩

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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)2c ⇒ ca
  2. abab2c ⇒ bac
  3. ba2 ⇒ c
  4. (ba)2c ⇒ cbab2c
  5. baca ⇒ cbabc
  6. cbab2a ⇒ bac
  7. cbab3ac ⇒ bacbab2c
  8. cbab2ca ⇒ bacbabc
  9. c(babc)2 ⇒ bac2a
  10. (cbab)2bc ⇒ (bac)2
  11. abab2a ⇒ c
  12. abab3ac ⇒ cbab2c 
# ab:ababba=baa bc/a baa=c magic:0
ababc=ca
ababbc=bac
baa=c
babac=cbabbc
baca=cbabc
cbabba=bac
cbabbbac=bacbabbc
cbabbca=bacbabc
cbabcbabc=bacca
cbabcbabbc=bacbac
ababba=c
ababbbac=cbabbc

Right Cayley graph (truncated)

Left Cayley graph (truncated)