#1293 ⟨a, b | aaaaabaaba=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. ca ⇒ ac
  2. cd ⇒ 1
  3. da ⇒ ad
  4. dc ⇒ 1
  5. a6 ⇒ c
  6. db ⇒ cbd2
  7. a2b ⇒ cba2d
  8. c2b ⇒ bc2
  9. a2cb ⇒ ba2c
  10. bcb ⇒ a4d 
# ab:aaaaabaaba=1 acd/b aaaaaa=c,baab=d magic:0
ca=ac
cd=1
da=ad
dc=1
aaaaaa=c
db=cbdd
aab=cbaad
ccb=bcc
aacb=baac
bcb=aaaad

Right Cayley graph (truncated)

Left Cayley graph (truncated)

Other isomorphic instances

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

2 total

Σ#PresentationMapping
101310⟨a, b | aaaabaabaa=1⟩φ(a) = a, φ(b) = b
101344⟨a, b | aaabaabaaa=1⟩φ(a) = a, φ(b) = b