#7179 ⟨a, b | ab=aa, bbb=aaa⟩

Up:Monoids with two generators and two relations
Prev:#7177 ⟨a, b | ab=aa, bba=baa⟩
Next:#7183 ⟨a, b | ab=aa, bbb=baa⟩

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. ab ⇒ a2
  2. b3 ⇒ a3
  3. ba3 ⇒ a4 
# ab:ab=aa,bbb=aaa ab
ab=aa
bbb=aaa
baaa=aaaa

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.

3 total

Σ#PresentationMapping
107180⟨a, b | ab=aa, bbb=aab⟩φ(a) = a, φ(b) = b
107181⟨a, b | ab=aa, bbb=aba⟩φ(a) = a, φ(b) = b
107182⟨a, b | ab=aa, bbb=abb⟩φ(a) = a, φ(b) = b