#1527 ⟨a, b | abbaaaaaab=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. cd ⇒ 1
  2. dc ⇒ 1
  3. ac ⇒ ca
  4. ad ⇒ da
  5. a6 ⇒ c
  6. cbab ⇒ bcba
  7. dbcb ⇒ babda5
  8. ab2 ⇒ bcbda
  9. c(ab)2 ⇒ abcba
  10. dabcb ⇒ (ab)2da5
  11. ca(ab)2 ⇒ a2bcba
  12. da2bcb ⇒ a(ab)2da5
  13. ca3bab ⇒ a3bcba
  14. da3bcb ⇒ a3babda5
  15. ca4bab ⇒ a4bcba
  16. da4bcb ⇒ a4babda5
  17. a5bcb ⇒ cb2a5
  18. a5bab ⇒ b2c
  19. b2cb ⇒ da5 
# ab:abbaaaaaab=1 cda/b aaaaaa=c,babb=d magic:0
cd=1
dc=1
ac=ca
ad=da
aaaaaa=c
cbab=bcba
dbcb=babdaaaaa
abb=bcbda
cabab=abcba
dabcb=ababdaaaaa
caabab=aabcba
daabcb=aababdaaaaa
caaabab=aaabcba
daaabcb=aaababdaaaaa
caaaabab=aaaabcba
daaaabcb=aaaababdaaaaa
aaaaabcb=cbbaaaaa
aaaaabab=bbc
bbcb=daaaaa

Right Cayley graph (truncated)

Left Cayley graph (truncated)