#4337 ⟨a, b | abbaabbba=ab⟩

Up:Monoids with two generators and one relation
Prev:#4336 ⟨a, b | abbaabbba=aa⟩
Next:#4338 ⟨a, b | abbaabbba=ba⟩

Quick links

  1. Properties
  2. Rewriting system

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. c3aca ⇒ c2a2c2 [15]
2. (cac)2a ⇒ caca2c2 [13]
3. c2a2c(ca)2 ⇒ caca2c2ac [14]
4. caca2c(ca)2 ⇒ c [12]
5. ab ⇒ c(aca)2 [7]
6. cb ⇒ caca2c2 [11]
# ab:abbaabbba=ab ac/b abbb=c morph:4/0
cccaca=ccaacc
caccaca=cacaacc
ccaaccaca=cacaaccac
cacaaccaca=c
ab=cacaaca
cb=cacaacc