#1693 ⟨a, b | abb=bb, bbb=b⟩

Up:Monoids with two generators and two relations
Prev:#1691 ⟨a, b | abb=ba, bbb=b⟩
Next:#1695 ⟨a, b | bab=aa, bbb=b⟩

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 ⇒ b [3]
2. b3 ⇒ b [2]
# ab:abb=bb,bbb=b ab
ab=b
bbb=b

Isomorphic instances

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

10 total

Σ#PresentationMapping
105141⟨a, b | aab=ab, abbb=b⟩φ(a) = a, φ(b) = b
1112254⟨a, b | aaab=ab, baaa=a⟩φ(a) = b, φ(b) = a
1112380⟨a, b | aaba=ba, abaa=a⟩φ(a) = b, φ(b) = a
1112388⟨a, b | aaba=ba, baaa=a⟩φ(a) = b, φ(b) = a
1112494⟨a, b | abaa=ba, baaa=a⟩φ(a) = b, φ(b) = a
1114573⟨a, b | aaba=a, baaba=a⟩φ(a) = b, φ(b) = a
1114577⟨a, b | aaba=a, babaa=a⟩φ(a) = b, φ(b) = a
1115624⟨a, b | aab=ab, aabbb=b⟩φ(a) = a, φ(b) = b
1115632⟨a, b | aab=ab, ababb=b⟩φ(a) = a, φ(b) = b
1115636⟨a, b | aab=ab, abbab=b⟩φ(a) = a, φ(b) = b