#20984 ⟨a, b | ab=aa, baaa=aaa⟩

Up:Monoids with two generators and two relations
Prev:#20927 ⟨a, b | ab=aa, aaaa=bbb⟩
Next:#20988 ⟨a, b | ab=aa, baaa=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. ba3 ⇒ a3
  3. a5 ⇒ a4 
# ab:ab=aa,baaa=aaa ab
ab=aa
baaa=aaa
aaaaa=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.

15 total

Σ#PresentationMapping
1120985⟨a, b | ab=aa, baaa=aab⟩φ(a) = a, φ(b) = b
1120986⟨a, b | ab=aa, baaa=aba⟩φ(a) = a, φ(b) = b
1120987⟨a, b | ab=aa, baaa=abb⟩φ(a) = a, φ(b) = b
1120992⟨a, b | ab=aa, baab=aaa⟩φ(a) = a, φ(b) = b
1120993⟨a, b | ab=aa, baab=aab⟩φ(a) = a, φ(b) = b
1120994⟨a, b | ab=aa, baab=aba⟩φ(a) = a, φ(b) = b
1120995⟨a, b | ab=aa, baab=abb⟩φ(a) = a, φ(b) = b
1121000⟨a, b | ab=aa, baba=aaa⟩φ(a) = a, φ(b) = b
1121001⟨a, b | ab=aa, baba=aab⟩φ(a) = a, φ(b) = b
1121002⟨a, b | ab=aa, baba=aba⟩φ(a) = a, φ(b) = b
1121003⟨a, b | ab=aa, baba=abb⟩φ(a) = a, φ(b) = b
1121008⟨a, b | ab=aa, babb=aaa⟩φ(a) = a, φ(b) = b
1121009⟨a, b | ab=aa, babb=aab⟩φ(a) = a, φ(b) = b
1121010⟨a, b | ab=aa, babb=aba⟩φ(a) = a, φ(b) = b
1121011⟨a, b | ab=aa, babb=abb⟩φ(a) = a, φ(b) = b