#21020 ⟨a, b | ab=aa, bbaa=baa⟩

Up:Monoids with two generators and two relations
Prev:#21016 ⟨a, b | ab=aa, bbaa=aaa⟩
Next:#21022 ⟨a, b | ab=aa, bbaa=bba⟩

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. b2a2 ⇒ ba2 [2]
3. a5 ⇒ a4 [3]
# ab:ab=aa,bbaa=baa ab
ab=aa
bbaa=baa
aaaaa=aaaa

Isomorphic instances

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

3 total

Σ#PresentationMapping
1121021⟨a, b | ab=aa, bbaa=bab⟩φ(a) = a, φ(b) = b
1121028⟨a, b | ab=aa, bbab=baa⟩φ(a) = a, φ(b) = b
1121029⟨a, b | ab=aa, bbab=bab⟩φ(a) = a, φ(b) = b