#9161 ⟨a, b | aa=a, abbb=bab⟩

Up:Monoids with two generators and two relations
Prev:#9159 ⟨a, b | aa=a, abbb=abb⟩
Next:#9162 ⟨a, b | aa=a, abbb=bba⟩

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. ab7 ⇒ ab5 [3]
2. bab ⇒ ab3 [2]
3. a2 ⇒ a [1]
# ab:aa=a,abbb=bab b/a
abbbbbbb=abbbbb
bab=abbb
aa=a

Isomorphic instances

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

2 total

Σ#PresentationMapping
1125173⟨a, b | aa=a, aabbb=bab⟩φ(a) = a, φ(b) = b
1125696⟨a, b | aa=a, baab=abbb⟩φ(a) = a, φ(b) = b