#3778 ⟨a, b | ababbaaaab=a⟩

Up:Monoids with two generators and one relation
Prev:#3777 ⟨a, b | abababbbba=b⟩
Next:#3779 ⟨a, b | ababbaaaab=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. a4c ⇒ aca3 [8]
2. aca3c ⇒ a [6]
3. aba3c ⇒ abca3 [7]
4. abca3c ⇒ ab [4]
5. a5b ⇒ aca3bca4 [10]
6. aca4b ⇒ abca4 [5]
7. ab2 ⇒ c [2]
8. aba4b ⇒ a(bca3)2a [9]
9. abca4b ⇒ a [3]
# ab:ababbaaaab=a ca/b abb=c morph:3/2
aaaac=acaaa
acaaac=a
abaaac=abcaaa
abcaaac=ab
aaaaab=acaaabcaaaa
acaaaab=abcaaaa
abb=c
abaaaab=abcaaabcaaaa
abcaaaab=a