#9474 ⟨a, b | aa=1, abbabbbb=1⟩

Up:Monoids with two generators and two relations
Prev:#9456 ⟨a, b | aa=1, abababab=1⟩
Next:#9478 ⟨a, b | aa=1, abbbabbb=1⟩

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 ⇒ 1
  2. b2a ⇒ ab2
  3. b6 ⇒ 1 
# ab:aa=1,abbabbbb=1 ab
aa=1
bba=abb
bbbbbb=1

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.

5 total

Σ#PresentationMapping
109480⟨a, b | aa=1, abbbbabb=1⟩φ(a) = a, φ(b) = b
109506⟨a, b | aa=1, babbabbb=1⟩φ(a) = a, φ(b) = b
109508⟨a, b | aa=1, babbbbab=1⟩φ(a) = a, φ(b) = b
109515⟨a, b | aa=1, bbabbabb=1⟩φ(a) = a, φ(b) = b
109794⟨a, b | aa=1, bbabbbb=a⟩φ(a) = a, φ(b) = b