#8085 ⟨a, b | aaa=1, babb=abb⟩

Up:Monoids with two generators and two relations
Prev:#8081 ⟨a, b | aaa=1, baab=bbb⟩
Next:#8087 ⟨a, b | aaa=1, babb=bab⟩

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. a3 ⇒ 1 [1]
2. b3 ⇒ b2 [4]
3. bab2 ⇒ ab2 [2]
4. ba2b2 ⇒ a2b2 [3]
# ab:aaa=1,babb=abb ab
aaa=1
bbb=bb
babb=abb
baabb=aabb

Isomorphic instances

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

2 total

Σ#PresentationMapping
1122234⟨a, b | aaa=1, aababb=bb⟩φ(a) = a, φ(b) = b
1122260⟨a, b | aaa=1, abaabb=bb⟩φ(a) = a, φ(b) = b