#2892 ⟨a, b | aa=a, bbabb=a⟩

Up:Monoids with two generators and two relations
Prev:#2891 ⟨a, b | aa=a, babbb=b⟩
Next:#2893 ⟨a, b | aa=a, bbabb=b⟩

Properties

Complete 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
  1. a2 ⇒ a
  2. b2a ⇒ ab2
  3. ab4 ⇒ a 
# ab:aa=a,bbabb=a ab
aa=a
bba=abb
abbbb=a

Right Cayley graph (truncated)

Left Cayley graph (truncated)

Other isomorphic instances

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

6 total

Σ#PresentationMapping
108634⟨a, b | aa=a, bbaabb=a⟩φ(a) = a, φ(b) = b
108906⟨a, b | aa=a, bbabb=aa⟩φ(a) = a, φ(b) = b
1115663⟨a, b | aab=ab, bbabb=a⟩φ(a) = a, φ(b) = b
1124176⟨a, b | aa=a, bbaaabb=a⟩φ(a) = a, φ(b) = b
1124714⟨a, b | aa=a, bbaabb=aa⟩φ(a) = a, φ(b) = b
1125248⟨a, b | aa=a, bbabb=aaa⟩φ(a) = a, φ(b) = b