#9260 ⟨a, b | ab=a, aaaa=baa⟩

Up:Monoids with two generators and two relations
Prev:#9256 ⟨a, b | ab=a, aaaa=aaa⟩
Next:#9262 ⟨a, b | ab=a, aaaa=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. a5 ⇒ a3 [3]
2. ba2 ⇒ a4 [2]
3. ab ⇒ a [1]
# ab:ab=a,aaaa=baa a/b
aaaaa=aaa
baa=aaaa
ab=a

Isomorphic instances

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

6 total

Σ#PresentationMapping
1125416⟨a, b | ab=a, aaaab=baa⟩φ(a) = a, φ(b) = b
1125424⟨a, b | ab=a, aaaba=baa⟩φ(a) = a, φ(b) = b
1125440⟨a, b | ab=a, aabaa=baa⟩φ(a) = a, φ(b) = b
1125472⟨a, b | ab=a, abaaa=baa⟩φ(a) = a, φ(b) = b
1125828⟨a, b | ab=a, baab=aaaa⟩φ(a) = a, φ(b) = b
1125837⟨a, b | ab=a, baba=aaaa⟩φ(a) = a, φ(b) = b