#755 ⟨a, b | aaa=1, bbbb=b⟩

Up:Monoids with two generators and two relations
Prev:#753 ⟨a, b | aaa=1, babb=b⟩
Next:#758 ⟨a, b | aab=1, aaab=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. a3 ⇒ 1 [1]
2. b4 ⇒ b [2]
# ab:aaa=1,bbbb=b ab
aaa=1
bbbb=b

Isomorphic instances

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

5 total

Σ#PresentationMapping
107801⟨a, b | aaa=1, abbbb=ab⟩φ(a) = a, φ(b) = b
1121679⟨a, b | aaa=1, aaabbbb=b⟩φ(a) = a, φ(b) = b
1121759⟨a, b | aaa=1, baaabbb=b⟩φ(a) = a, φ(b) = b
1121781⟨a, b | aaa=1, bbaaabb=b⟩φ(a) = a, φ(b) = b
1123322⟨a, b | aaa=1, bbbb=aaab⟩φ(a) = a, φ(b) = b