#652 ⟨a, b | aaabbbbba=1⟩

Up:Monoids with two generators and one relation
Prev:#651 ⟨a, b | aaabbbbab=1⟩
Next:#655 ⟨a, b | aabaaaabb=1⟩

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. cb ⇒ bc
  3. cd ⇒ 1
  4. da ⇒ ad
  5. db ⇒ bd
  6. dc ⇒ 1
  7. a4 ⇒ c
  8. b5 ⇒ d 
# ab:aaabbbbba=1 abcd aaaa=c,bbbbb=d magic:0
ca=ac
cb=bc
cd=1
da=ad
db=bd
dc=1
aaaa=c
bbbbb=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
9692⟨a, b | aabbbbbaa=1⟩φ(a) = a, φ(b) = b