#2083 ⟨a, b | aab=b, bbbb=b⟩

Up:Monoids with two generators and two relations
Prev:#2081 ⟨a, b | aab=b, bbba=b⟩
Next:#2084 ⟨a, b | aba=a, aaaa=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. a2b ⇒ b
  2. b4 ⇒ b 
# ab:aab=b,bbbb=b ab
aab=b
bbbb=b

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.

7 total

Σ#PresentationMapping
1112489⟨a, b | aabb=bb, bbbb=b⟩φ(a) = a, φ(b) = b
1118991⟨a, b | aab=b, aabbbb=b⟩φ(a) = a, φ(b) = b
1119039⟨a, b | aab=b, baabbb=b⟩φ(a) = a, φ(b) = b
1119063⟨a, b | aab=b, bbaabb=b⟩φ(a) = a, φ(b) = b
1119075⟨a, b | aab=b, bbbaab=b⟩φ(a) = a, φ(b) = b
1119565⟨a, b | aab=b, abbbb=ab⟩φ(a) = a, φ(b) = b
1120169⟨a, b | aab=b, bbbb=aab⟩φ(a) = a, φ(b) = b