#948 ⟨a, b | ab=a, bbba=a⟩

Up:Monoids with two generators and two relations
Prev:#944 ⟨a, b | ab=a, bbaa=a⟩
Next:#950 ⟨a, b | ab=a, bbbb=a⟩

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. b3a ⇒ a [2]
# ab:ab=a,bbba=a ab
ab=a
bbba=a

Isomorphic instances

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

12 total

Σ#PresentationMapping
92994⟨a, b | ab=a, bbbab=a⟩φ(a) = a, φ(b) = b
93129⟨a, b | ab=a, bbba=ab⟩φ(a) = a, φ(b) = b
105245⟨a, b | aba=ab, aaab=b⟩φ(a) = b, φ(b) = a
108830⟨a, b | ab=a, bbbabb=a⟩φ(a) = a, φ(b) = b
109101⟨a, b | ab=a, bbbab=ab⟩φ(a) = a, φ(b) = b
109371⟨a, b | ab=a, bbba=abb⟩φ(a) = a, φ(b) = b
1114478⟨a, b | aaab=b, aaaba=b⟩φ(a) = b, φ(b) = a
1115846⟨a, b | aba=ab, aaaba=b⟩φ(a) = b, φ(b) = a
1124570⟨a, b | ab=a, bbbabbb=a⟩φ(a) = a, φ(b) = b
1125097⟨a, b | ab=a, bbbabb=ab⟩φ(a) = a, φ(b) = b
1125639⟨a, b | ab=a, bbbab=abb⟩φ(a) = a, φ(b) = b
1125890⟨a, b | ab=a, bbba=abbb⟩φ(a) = a, φ(b) = b