#20786 ⟨a, b | ab=aa, baaaa=ba⟩

Up:Monoids with two generators and two relations
Prev:#20784 ⟨a, b | ab=aa, baaaa=aa⟩
Next:#20787 ⟨a, b | ab=aa, baaaa=bb⟩

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 ⇒ a2 [1]
2. ba4 ⇒ ba [2]
3. a6 ⇒ a3 [3]
# ab:ab=aa,baaaa=ba ab
ab=aa
baaaa=ba
aaaaaa=aaa

Isomorphic instances

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

7 total

Σ#PresentationMapping
1120790⟨a, b | ab=aa, baaab=ba⟩φ(a) = a, φ(b) = b
1120794⟨a, b | ab=aa, baaba=ba⟩φ(a) = a, φ(b) = b
1120798⟨a, b | ab=aa, baabb=ba⟩φ(a) = a, φ(b) = b
1120802⟨a, b | ab=aa, babaa=ba⟩φ(a) = a, φ(b) = b
1120806⟨a, b | ab=aa, babab=ba⟩φ(a) = a, φ(b) = b
1120810⟨a, b | ab=aa, babba=ba⟩φ(a) = a, φ(b) = b
1120814⟨a, b | ab=aa, babbb=ba⟩φ(a) = a, φ(b) = b