#9262 ⟨a, b | ab=a, aaaa=bba⟩

Up:Monoids with two generators and two relations
Prev:#9260 ⟨a, b | ab=a, aaaa=baa⟩
Next:#9263 ⟨a, b | ab=a, aaaa=bbb⟩

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 ⇒ a2 [3]
2. ab ⇒ a [1]
3. b2a ⇒ a4 [2]
# ab:ab=a,aaaa=bba a/b
aaaaa=aa
ab=a
bba=aaaa

Isomorphic instances

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

5 total

Σ#PresentationMapping
1125418⟨a, b | ab=a, aaaab=bba⟩φ(a) = a, φ(b) = b
1125426⟨a, b | ab=a, aaaba=bba⟩φ(a) = a, φ(b) = b
1125442⟨a, b | ab=a, aabaa=bba⟩φ(a) = a, φ(b) = b
1125474⟨a, b | ab=a, abaaa=bba⟩φ(a) = a, φ(b) = b
1125870⟨a, b | ab=a, bbab=aaaa⟩φ(a) = a, φ(b) = b