#613 ⟨a, b | aaaabaaba=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. a5 ⇒ c
  6. ab ⇒ dbca
  7. c2b ⇒ dbc3
  8. d2b ⇒ cbd3
  9. bcb ⇒ da3 
# ab:aaaabaaba=1 cda/b aaaaa=c,baab=d magic:0
cd=1
dc=1
ac=ca
ad=da
aaaaa=c
ab=dbca
ccb=dbccc
ddb=cbddd
bcb=daaa

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
9629⟨a, b | aaabaabaa=1⟩φ(a) = a, φ(b) = b
9653⟨a, b | aabaaaaab=1⟩φ(a) = a, φ(b) = b