#998 ⟨a, b | ab=a, aab=ba⟩

Up:Monoids with two generators and two relations
Prev:#995 ⟨a, b | ab=a, aaa=bb⟩
Next:#1008 ⟨a, b | ab=a, baa=aa⟩

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. ba ⇒ a2
  3. a3 ⇒ a2 
# ab:ab=a,aab=ba ab
ab=a
ba=aa
aaa=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.

33 total

Σ#PresentationMapping
81002⟨a, b | ab=a, aba=ba⟩φ(a) = a, φ(b) = b
81012⟨a, b | ab=a, bab=aa⟩φ(a) = a, φ(b) = b
93086⟨a, b | ab=a, aabb=ba⟩φ(a) = a, φ(b) = b
93094⟨a, b | ab=a, abab=ba⟩φ(a) = a, φ(b) = b
93098⟨a, b | ab=a, abba=ba⟩φ(a) = a, φ(b) = b
93116⟨a, b | ab=a, babb=aa⟩φ(a) = a, φ(b) = b
93183⟨a, b | ab=a, bab=aab⟩φ(a) = a, φ(b) = b
93184⟨a, b | ab=a, bab=aba⟩φ(a) = a, φ(b) = b
109014⟨a, b | ab=a, aabbb=ba⟩φ(a) = a, φ(b) = b
109030⟨a, b | ab=a, ababb=ba⟩φ(a) = a, φ(b) = b
109038⟨a, b | ab=a, abbab=ba⟩φ(a) = a, φ(b) = b
109042⟨a, b | ab=a, abbba=ba⟩φ(a) = a, φ(b) = b
109076⟨a, b | ab=a, babbb=aa⟩φ(a) = a, φ(b) = b
109285⟨a, b | ab=a, aabb=bab⟩φ(a) = a, φ(b) = b
109301⟨a, b | ab=a, abab=bab⟩φ(a) = a, φ(b) = b
109309⟨a, b | ab=a, abba=bab⟩φ(a) = a, φ(b) = b
109345⟨a, b | ab=a, babb=aab⟩φ(a) = a, φ(b) = b
109346⟨a, b | ab=a, babb=aba⟩φ(a) = a, φ(b) = b
1124922⟨a, b | ab=a, aabbbb=ba⟩φ(a) = a, φ(b) = b
1124954⟨a, b | ab=a, ababbb=ba⟩φ(a) = a, φ(b) = b
1124970⟨a, b | ab=a, abbabb=ba⟩φ(a) = a, φ(b) = b
1124978⟨a, b | ab=a, abbbab=ba⟩φ(a) = a, φ(b) = b
1124982⟨a, b | ab=a, abbbba=ba⟩φ(a) = a, φ(b) = b
1125048⟨a, b | ab=a, babbbb=aa⟩φ(a) = a, φ(b) = b
1125465⟨a, b | ab=a, aabbb=bab⟩φ(a) = a, φ(b) = b
1125497⟨a, b | ab=a, ababb=bab⟩φ(a) = a, φ(b) = b
1125513⟨a, b | ab=a, abbab=bab⟩φ(a) = a, φ(b) = b
1125521⟨a, b | ab=a, abbba=bab⟩φ(a) = a, φ(b) = b
1125589⟨a, b | ab=a, babbb=aab⟩φ(a) = a, φ(b) = b
1125590⟨a, b | ab=a, babbb=aba⟩φ(a) = a, φ(b) = b
1125850⟨a, b | ab=a, babb=aabb⟩φ(a) = a, φ(b) = b
1125852⟨a, b | ab=a, babb=abab⟩φ(a) = a, φ(b) = b
1125853⟨a, b | ab=a, babb=abba⟩φ(a) = a, φ(b) = b