#91 ⟨a, b | ababa=b⟩

Up:Monoids with two generators and one relation
Prev:#90 ⟨a, b | ababa=a⟩
Next:#92 ⟨a, b | abbba=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. b2a ⇒ ab2
  2. a(ba)2 ⇒ b 
# ab:ababa=b ab
bba=abb
ababa=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.

4 total

Σ#PresentationMapping
7190⟨a, b | abaaba=b⟩φ(a) = a, φ(b) = abab
8396⟨a, b | abaaaba=b⟩φ(a) = a, φ(b) = bab
9834⟨a, b | abaaaaba=b⟩φ(a) = a, φ(b) = baabab
101750⟨a, b | abaaaaaba=b⟩φ(a) = a, φ(b) = baabaabab