#9048 ⟨a, b | ab=a, baaaa=aa⟩

Up:Monoids with two generators and two relations
Prev:#8987 ⟨a, b | ab=a, aaaaa=bb⟩
Next:#9050 ⟨a, b | ab=a, baaaa=ba⟩

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 ⇒ a
  2. ba2 ⇒ a2
  3. a4 ⇒ a2 
# ab:ab=a,baaaa=aa ab
ab=a
baa=aa
aaaa=aa

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.

6 total

Σ#PresentationMapping
1124992⟨a, b | ab=a, baaaab=aa⟩φ(a) = a, φ(b) = b
1124996⟨a, b | ab=a, baaaba=aa⟩φ(a) = a, φ(b) = b
1125004⟨a, b | ab=a, baabaa=aa⟩φ(a) = a, φ(b) = b
1125020⟨a, b | ab=a, babaaa=aa⟩φ(a) = a, φ(b) = b
1125533⟨a, b | ab=a, baaaa=aab⟩φ(a) = a, φ(b) = b
1125534⟨a, b | ab=a, baaaa=aba⟩φ(a) = a, φ(b) = b