#3931 ⟨a, b | abab=aa, bbbb=1⟩

Up:Monoids with two generators and two relations
Prev:#3914 ⟨a, b | aabb=ba, bbbb=1⟩
Next:#3940 ⟨a, b | abab=ba, abba=1⟩

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. b4 ⇒ 1 [2]
2. aba ⇒ a2b3 [4]
3. a2b3a ⇒ a3b [5]
4. a3b2a ⇒ a4b2 [6]
# ab:abab=aa,bbbb=1 b/a
bbbb=1
aba=aabbb
aabbba=aaab
aaabba=aaaabb