#1970 ⟨a, b | aababbaa=ab⟩

Up:Monoids with two generators and one relation
Prev:#1969 ⟨a, b | aababbaa=aa⟩
Next:#1971 ⟨a, b | aababbaa=ba⟩

Properties

Complete 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
  1. ab ⇒ c
  2. cb2 ⇒ c3bac
  3. ac2bac ⇒ cb
  4. c3ba2 ⇒ cb
  5. (cb)2ac ⇒ ac(cb)2
  6. cbc2bac ⇒ c3bacb
  7. ac2ba2 ⇒ c
  8. (cb)2a2 ⇒ ac2bc
  9. cbc2ba2 ⇒ c3bac 
# ab:aababbaa=ab c/ab ab=c magic:0
ab=c
cbb=cccbac
accbac=cb
cccbaa=cb
cbcbac=accbcb
cbccbac=cccbacb
accbaa=c
cbcbaa=accbc
cbccbaa=cccbac

Right Cayley graph (truncated)

Left Cayley graph (truncated)