#24173 ⟨a, b | aa=a, babbbab=b⟩

Up:Monoids with two generators and two relations
Prev:#24172 ⟨a, b | aa=a, babbbab=a⟩
Next:#24174 ⟨a, b | aa=a, babbbbb=a⟩

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. b2 ⇒ c [3]
2. cb ⇒ bc [5]
3. a2 ⇒ a [1]
4. babc ⇒ bcab [9]
5. bac2 ⇒ bcac [14]
6. cabc ⇒ c2ab [10]
7. cac2 ⇒ c2ac [16]
8. c(ab)2 ⇒ (ba)2c [19]
9. cabac ⇒ b [20]
# ab:aa=a,babbbab=b bca bb=c morph:2/0
bb=c
cb=bc
aa=a
babc=bcab
bacc=bcac
cabc=ccab
cacc=ccac
cabab=babac
cabac=b

Isomorphic instances

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

1 total

Σ#PresentationMapping
1124181⟨a, b | aa=a, bbababb=b⟩φ(a) = a, φ(b) = b