#2156 ⟨a, b | ba=ab, aaaaa=1⟩

Up:Monoids with two generators and two relations
Prev:#2123 ⟨a, b | aba=b, bbbb=b⟩
Next:#2176 ⟨a, b | ab=aa, 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. ba ⇒ ab
  2. a5 ⇒ 1 
# ab:ba=ab,aaaaa=1 ab
ba=ab
aaaaa=1

Staircase diagram

Right Cayley graph (truncated)

Other isomorphic instances

The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.

2 total

Σ#PresentationMapping
1112692⟨a, b | aba=aab, aaaaa=1⟩φ(a) = a, φ(b) = b
1112804⟨a, b | baa=aab, aaaaa=1⟩φ(a) = a, φ(b) = b