#9352 ⟨a, b | ab=a, bbaa=aaa⟩

Up:Monoids with two generators and two relations
Prev:#9327 ⟨a, b | ab=a, baaa=bbb⟩
Next:#9356 ⟨a, b | ab=a, bbaa=baa⟩

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. a4 ⇒ a3 [3]
3. b2a2 ⇒ a3 [2]
# ab:ab=a,bbaa=aaa ab
ab=a
aaaa=aaa
bbaa=aaa

Isomorphic instances

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

5 total

Σ#PresentationMapping
1125604⟨a, b | ab=a, bbaab=aaa⟩φ(a) = a, φ(b) = b
1125612⟨a, b | ab=a, bbaba=aaa⟩φ(a) = a, φ(b) = b
1125859⟨a, b | ab=a, bbaa=aaab⟩φ(a) = a, φ(b) = b
1125860⟨a, b | ab=a, bbaa=aaba⟩φ(a) = a, φ(b) = b
1125862⟨a, b | ab=a, bbaa=abaa⟩φ(a) = a, φ(b) = b