#1059 ⟨a, b | aa=1, bbbbbb=1⟩

Up:Monoids with two generators and two relations
Prev:#1046 ⟨a, b | aa=1, abbabb=1⟩
Next:#1117 ⟨a, b | aa=1, ababb=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. a2 ⇒ 1
  2. b6 ⇒ 1 
# ab:aa=1,bbbbbb=1 ab
aa=1
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.

8 total

Σ#PresentationMapping
106165⟨a, b | aab=b, bbbbbb=1⟩φ(a) = a, φ(b) = b
109441⟨a, b | aa=1, aabbbbbb=1⟩φ(a) = a, φ(b) = b
109482⟨a, b | aa=1, abbbbbba=1⟩φ(a) = a, φ(b) = b
109498⟨a, b | aa=1, baabbbbb=1⟩φ(a) = a, φ(b) = b
109513⟨a, b | aa=1, bbaabbbb=1⟩φ(a) = a, φ(b) = b
109517⟨a, b | aa=1, bbbaabbb=1⟩φ(a) = a, φ(b) = b
109758⟨a, b | aa=1, abbbbbb=a⟩φ(a) = a, φ(b) = b
1010061⟨a, b | aa=1, bbbbbb=aa⟩φ(a) = a, φ(b) = b