#1010 ⟨a, b | ab=a, baa=ba⟩

Up:Monoids with two generators and two relations
Prev:#1008 ⟨a, b | ab=a, baa=aa⟩
Next:#1011 ⟨a, b | ab=a, baa=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. ab ⇒ a
  2. a3 ⇒ a2
  3. ba2 ⇒ ba 
# ab:ab=a,baa=ba ab
ab=a
aaa=aa
baa=ba

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.

19 total

Σ#PresentationMapping
93110⟨a, b | ab=a, baab=ba⟩φ(a) = a, φ(b) = b
93114⟨a, b | ab=a, baba=ba⟩φ(a) = a, φ(b) = b
93186⟨a, b | ab=a, bab=baa⟩φ(a) = a, φ(b) = b
109062⟨a, b | ab=a, baabb=ba⟩φ(a) = a, φ(b) = b
109070⟨a, b | ab=a, babab=ba⟩φ(a) = a, φ(b) = b
109074⟨a, b | ab=a, babba=ba⟩φ(a) = a, φ(b) = b
109333⟨a, b | ab=a, baab=bab⟩φ(a) = a, φ(b) = b
109341⟨a, b | ab=a, baba=bab⟩φ(a) = a, φ(b) = b
109348⟨a, b | ab=a, babb=baa⟩φ(a) = a, φ(b) = b
1125018⟨a, b | ab=a, baabbb=ba⟩φ(a) = a, φ(b) = b
1125034⟨a, b | ab=a, bababb=ba⟩φ(a) = a, φ(b) = b
1125042⟨a, b | ab=a, babbab=ba⟩φ(a) = a, φ(b) = b
1125046⟨a, b | ab=a, babbba=ba⟩φ(a) = a, φ(b) = b
1125561⟨a, b | ab=a, baabb=bab⟩φ(a) = a, φ(b) = b
1125577⟨a, b | ab=a, babab=bab⟩φ(a) = a, φ(b) = b
1125585⟨a, b | ab=a, babba=bab⟩φ(a) = a, φ(b) = b
1125592⟨a, b | ab=a, babbb=baa⟩φ(a) = a, φ(b) = b
1125856⟨a, b | ab=a, babb=baab⟩φ(a) = a, φ(b) = b
1125857⟨a, b | ab=a, babb=baba⟩φ(a) = a, φ(b) = b