#310 ⟨a, b | aababbba=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. b3c ⇒ a2bab2
  9. bab2d ⇒ adb3
  10. b3ac ⇒ a2bab2a
  11. bab2ad ⇒ adb3a
  12. b3a2 ⇒ a2db2cb
  13. bab2a2 ⇒ db(bc)2
  14. bab3 ⇒ d 
# ab:aababbba=1 reversed:cda/b aaa=c,babbb=d magic:0
dc=1
cd=1
ca=ac
da=ad
aaa=c
bcba=cbab
babaa=dbcbc
bbbc=aababb
babbd=adbbb
bbbac=aababba
babbad=adbbba
bbbaa=aadbbcb
babbaa=dbbcbc
babbb=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
8317⟨a, b | aabbbaba=1⟩φ(a) = a, φ(b) = b