#12906 ⟨a, b | aab=aaa, bbab=a⟩

Up:Monoids with two generators and two relations
Prev:#12903 ⟨a, b | aab=aaa, babb=b⟩
Next:#12907 ⟨a, b | aab=aaa, bbab=b⟩

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. a2b ⇒ a3 [1]
2. b2a2 ⇒ (ab)2 [3]
3. b2ab ⇒ a [2]
4. a(ba)2 ⇒ aba3 [8]
5. abab2 ⇒ aba3 [10]
6. a6 ⇒ a3 [4]
7. aba5 ⇒ aba2 [9]
# ab:aab=aaa,bbab=a ab
aab=aaa
bbaa=abab
bbab=a
ababa=abaaa
ababb=abaaa
aaaaaa=aaa
abaaaaa=abaa