#1016 ⟨a, b | ab=a, bba=aa⟩

Up:Monoids with two generators and two relations
Prev:#1011 ⟨a, b | ab=a, baa=bb⟩
Next:#1018 ⟨a, b | ab=a, bba=ba⟩

Quick links

  1. Properties
  2. Rewriting system
  3. Isomorphic instances

Properties

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
#RuleProof
1. ab ⇒ a [1]
2. a3 ⇒ a2 [3]
3. b2a ⇒ a2 [2]
# ab:ab=a,bba=aa ab
ab=a
aaa=aa
bba=aa

Isomorphic instances

The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.

19 total

Σ#PresentationMapping
93124⟨a, b | ab=a, bbab=aa⟩φ(a) = a, φ(b) = b
93188⟨a, b | ab=a, bba=aab⟩φ(a) = a, φ(b) = b
93189⟨a, b | ab=a, bba=aba⟩φ(a) = a, φ(b) = b
109092⟨a, b | ab=a, bbabb=aa⟩φ(a) = a, φ(b) = b
109286⟨a, b | ab=a, aabb=bba⟩φ(a) = a, φ(b) = b
109302⟨a, b | ab=a, abab=bba⟩φ(a) = a, φ(b) = b
109310⟨a, b | ab=a, abba=bba⟩φ(a) = a, φ(b) = b
109361⟨a, b | ab=a, bbab=aab⟩φ(a) = a, φ(b) = b
109362⟨a, b | ab=a, bbab=aba⟩φ(a) = a, φ(b) = b
1125080⟨a, b | ab=a, bbabbb=aa⟩φ(a) = a, φ(b) = b
1125466⟨a, b | ab=a, aabbb=bba⟩φ(a) = a, φ(b) = b
1125498⟨a, b | ab=a, ababb=bba⟩φ(a) = a, φ(b) = b
1125514⟨a, b | ab=a, abbab=bba⟩φ(a) = a, φ(b) = b
1125522⟨a, b | ab=a, abbba=bba⟩φ(a) = a, φ(b) = b
1125621⟨a, b | ab=a, bbabb=aab⟩φ(a) = a, φ(b) = b
1125622⟨a, b | ab=a, bbabb=aba⟩φ(a) = a, φ(b) = b
1125873⟨a, b | ab=a, bbab=aabb⟩φ(a) = a, φ(b) = b
1125875⟨a, b | ab=a, bbab=abab⟩φ(a) = a, φ(b) = b
1125876⟨a, b | ab=a, bbab=abba⟩φ(a) = a, φ(b) = b