#1506 ⟨a, b | ababaaabab=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. a3 ⇒ c
  6. cb ⇒ aba2
  7. db ⇒ aba2d2
  8. a2b ⇒ ba2
  9. b(ab)3 ⇒ d 
# ab:ababaaabab=1 acd/b aaa=c,bababab=d magic:0
ca=ac
cd=1
da=ad
dc=1
aaa=c
cb=abaa
db=abaadd
aab=baa
bababab=d

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.

1 total

Σ#PresentationMapping
101511⟨a, b | abababaaab=1⟩φ(a) = a, φ(b) = b