#685 ⟨a, b | aabbabbba=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. dc ⇒ 1
  2. cd ⇒ 1
  3. ca ⇒ ac
  4. da ⇒ ad
  5. a3 ⇒ c
  6. b3c ⇒ a2b2ab
  7. b2abd ⇒ adb3
  8. bcb2a ⇒ cb2ab
  9. b3ac ⇒ a2b(ba)2
  10. b(ba)2d ⇒ adb3a
  11. b3a2 ⇒ a2dbcb2
  12. b2aba2 ⇒ dbcb2c
  13. b2ab2d ⇒ dbab3
  14. (b2a)2d ⇒ dbab3a
  15. (b2a)2a ⇒ d(b2c)2
  16. b2ab3 ⇒ d 
# ab:aabbabbba=1 reversed:cda/b aaa=c,bbabbb=d magic:0
dc=1
cd=1
ca=ac
da=ad
aaa=c
bbbc=aabbab
bbabd=adbbb
bcbba=cbbab
bbbac=aabbaba
bbabad=adbbba
bbbaa=aadbcbb
bbabaa=dbcbbc
bbabbd=dbabbb
bbabbad=dbabbba
bbabbaa=dbbcbbc
bbabbb=d

Right Cayley graph (truncated)

Left Cayley graph (truncated)

Other anti-isomorphic instances

The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.

1 total

Σ#PresentationMapping
9689⟨a, b | aabbbabba=1⟩φ(a) = a, φ(b) = b