#19554 ⟨a, b | aab=b, abbaa=ba⟩

Up:Monoids with two generators and two relations
Prev:#19552 ⟨a, b | aab=b, abbaa=aa⟩
Next:#19555 ⟨a, b | aab=b, abbaa=bb⟩

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. b5 ⇒ b2
  2. bab ⇒ ab3
  3. b4a ⇒ ba
  4. a2b ⇒ b
  5. ba2 ⇒ ab2a 
# ab:aab=b,abbaa=ba b/a
bbbbb=bb
bab=abbb
bbbba=ba
aab=b
baa=abba

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
1120146⟨a, b | aab=b, bbaa=aba⟩φ(a) = a, φ(b) = b