#1082 ⟨a, b | aabbaa=aab⟩

Up:Monoids with two generators and one relation
Prev:#1081 ⟨a, b | aabbaa=aaa⟩
Next:#1083 ⟨a, b | aabbaa=aba⟩

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. cb ⇒ c2
  2. a2b ⇒ a2c
  3. cab ⇒ cac
  4. b2a2 ⇒ c
  5. c3a2 ⇒ c2
  6. a2c2a2 ⇒ a2c
  7. cac2a2 ⇒ cac 
# ab:aabbaa=aab acb bbaa=c frequency:4/0
cb=cc
aab=aac
cab=cac
bbaa=c
cccaa=cc
aaccaa=aac
caccaa=cac

Right Cayley graph (truncated)

Left Cayley graph (truncated)