#27167 ⟨a, b | aa=1, abbbbbb=bb⟩

Up:Monoids with two generators and two relations
Prev:#27163 ⟨a, b | aa=1, abbbbba=bb⟩
Next:#27204 ⟨a, b | aa=1, bababab=bb⟩

Quick links

  1. Properties
  2. Rewriting system
  3. Isomorphic instances

Properties

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
#RuleProof
1. b10 ⇒ b2 [4]
2. ab2 ⇒ b6 [3]
3. a2 ⇒ 1 [1]
# ab:aa=1,abbbbbb=bb b/a
bbbbbbbbbb=bb
abb=bbbbbb
aa=1

Isomorphic instances

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

1 total

Σ#PresentationMapping
1127765⟨a, b | aa=1, bbbbbb=abb⟩φ(a) = a, φ(b) = b