#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⟩

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. a4 ⇒ a2 [2]
2. b2 ⇒ aba [1]
3. (ab)2 ⇒ (ba)2 [3]
4. baba2b ⇒ (a2b)2a [4]
5. baba3b ⇒ a(a2b)2a [6]
6. ab(a2b)2 ⇒ b(a2b)2a [5]
7. aba2ba3b ⇒ ba(a2b)2a [7]
8. (a3b)2a2ba ⇒ (aba2)2ba [8]
# ab:aba=bb,aaaa=aa a/b
aaaa=aa
bb=aba
abab=baba
babaab=aabaaba
babaaab=aaabaaba
abaabaab=baabaaba
abaabaaab=baaabaaba
aaabaaabaaba=abaaabaaba