#16437 ⟨a, b | aba=bb, aaaa=aa⟩

Up:Monoids with two generators and two relations
Prev:#16436 ⟨a, b | aba=ab, bbbb=bb⟩
Next:#16439 ⟨a, b | aba=bb, aaaa=bb⟩

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. a4 ⇒ a2
  2. b2 ⇒ aba
  3. (ab)2 ⇒ (ba)2
  4. baba2b ⇒ (a2b)2a
  5. baba3b ⇒ a(a2b)2a
  6. ab(a2b)2 ⇒ b(a2b)2a
  7. aba2ba3b ⇒ ba(a2b)2a
  8. (a3b)2a2ba ⇒ (aba2)2ba 
# ab:aba=bb,aaaa=aa a/b
aaaa=aa
bb=aba
abab=baba
babaab=aabaaba
babaaab=aaabaaba
abaabaab=baabaaba
abaabaaab=baaabaaba
aaabaaabaaba=abaaabaaba

Right Cayley graph (truncated)

Left Cayley graph (truncated)