#678 ⟨a, b | aabbaaabb=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. ac ⇒ ca
  2. dc ⇒ 1
  3. ad ⇒ da
  4. cd ⇒ 1
  5. a3 ⇒ c
  6. ba2 ⇒ ca2bd
  7. bda ⇒ d2abc
  8. bc2 ⇒ ca2ba
  9. bd2 ⇒ d4a2bca
  10. bca2 ⇒ ca2b
  11. b2a ⇒ ab2
  12. b2c ⇒ cb2
  13. b2d ⇒ db2
  14. b4 ⇒ d2a 
# ab:aabbaaabb=1 reversed:acd/b aaa=c,bbaabb=d magic:0
ac=ca
dc=1
ad=da
cd=1
aaa=c
baa=caabd
bda=ddabc
bcc=caaba
bdd=ddddaabca
bcaa=caab
bba=abb
bbc=cbb
bbd=dbb
bbbb=dda

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
9680⟨a, b | aabbaabba=1⟩φ(a) = a, φ(b) = b