#3858 ⟨a, b | aaba=ab, bbbb=1⟩

Up:Monoids with two generators and two relations
Prev:#3845 ⟨a, b | aaba=aa, bbbb=1⟩
Next:#3871 ⟨a, b | aaba=ba, bbbb=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. a2ba ⇒ ab [1]
2. ab2a ⇒ a2b2 [4]
3. b4 ⇒ 1 [2]
4. a(ba)2 ⇒ ab2 [3]
5. ab3a ⇒ abab2 [5]
# ab:aaba=ab,bbbb=1 ab
aaba=ab
abba=aabb
bbbb=1
ababa=abb
abbba=ababb