#2876 ⟨a, b | aa=a, ababb=a⟩

Up:Monoids with two generators and two relations
Prev:#2874 ⟨a, b | aa=a, ababa=a⟩
Next:#2878 ⟨a, b | aa=a, abbab=a⟩

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. abab2 ⇒ a 
# ab:aa=a,ababb=a ab
aa=a
ababb=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.

10 total

Σ#PresentationMapping
108588⟨a, b | aa=a, aababb=a⟩φ(a) = a, φ(b) = b
108602⟨a, b | aa=a, abaabb=a⟩φ(a) = a, φ(b) = b
108877⟨a, b | aa=a, ababb=aa⟩φ(a) = a, φ(b) = b
1115631⟨a, b | aab=ab, ababb=a⟩φ(a) = a, φ(b) = b
1124066⟨a, b | aa=a, aaababb=a⟩φ(a) = a, φ(b) = b
1124080⟨a, b | aa=a, aabaabb=a⟩φ(a) = a, φ(b) = b
1124108⟨a, b | aa=a, abaaabb=a⟩φ(a) = a, φ(b) = b
1124627⟨a, b | aa=a, aababb=aa⟩φ(a) = a, φ(b) = b
1124653⟨a, b | aa=a, abaabb=aa⟩φ(a) = a, φ(b) = b
1125190⟨a, b | aa=a, ababb=aaa⟩φ(a) = a, φ(b) = b