#1436 ⟨a, b | aababbbbba=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. bcba ⇒ cbab
  7. baba2 ⇒ d(bc)2
  8. bab2a2 ⇒ db(bc)2
  9. bab3a2 ⇒ db3cbc
  10. b5c ⇒ a2bab4
  11. bab4d ⇒ adb5
  12. b5ac ⇒ a2bab4a
  13. bab4ad ⇒ adb5a
  14. b5a2 ⇒ a2db4cb
  15. bab4a2 ⇒ db4cbc
  16. bab5 ⇒ d 
# ab:aababbbbba=1 reversed:cda/b aaa=c,babbbbb=d magic:0
dc=1
cd=1
ca=ac
da=ad
aaa=c
bcba=cbab
babaa=dbcbc
babbaa=dbbcbc
babbbaa=dbbbcbc
bbbbbc=aababbbb
babbbbd=adbbbbb
bbbbbac=aababbbba
babbbbad=adbbbbba
bbbbbaa=aadbbbbcb
babbbbaa=dbbbbcbc
babbbbb=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
101471⟨a, b | aabbbbbaba=1⟩φ(a) = a, φ(b) = b