#16063 ⟨a, b | aaa=bb, abab=bb⟩

Up:Monoids with two generators and two relations
Prev:#16061 ⟨a, b | aaa=bb, abab=ab⟩
Next:#16067 ⟨a, b | aaa=bb, abbb=aa⟩

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. a11 ⇒ a5
  2. ba9 ⇒ ba3
  3. aba3 ⇒ ba8
  4. a3b ⇒ ba3
  5. b2 ⇒ a3
  6. (ab)2 ⇒ a3 
# ab:aaa=bb,abab=bb a/b
aaaaaaaaaaa=aaaaa
baaaaaaaaa=baaa
abaaa=baaaaaaaa
aaab=baaa
bb=aaa
abab=aaa

Right Cayley graph (truncated)

Left Cayley graph (truncated)