#4678 ⟨a, b | aaab=b, aabb=b⟩

Up:Monoids with two generators and two relations
Prev:#4673 ⟨a, b | aaab=a, bbba=a⟩
Next:#4680 ⟨a, b | aaab=b, abaa=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. ab ⇒ b2
  2. b4 ⇒ b 
# ab:aaab=b,aabb=b ba
ab=bb
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.

3 total

Σ#PresentationMapping
104682⟨a, b | aaab=b, abab=b⟩φ(a) = a, φ(b) = b
104708⟨a, b | aaba=a, baba=a⟩φ(a) = b, φ(b) = a
1112999⟨a, b | abb=aab, aaab=b⟩φ(a) = a, φ(b) = b