#4768 ⟨a, b | abaaabab=aab⟩

Up:Monoids with two generators and one relation
Prev:#4767 ⟨a, b | abaaabab=aaa⟩
Next:#4769 ⟨a, b | abaaabab=aba⟩

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. a2c ⇒ c2 [9]
2. cac ⇒ ac2 [10]
3. a2b ⇒ cb [3]
4. cab ⇒ acb [14]
5. c2ba ⇒ abc2 [11]
6. c2bc ⇒ abac2 [13]
7. abacba ⇒ c [4]
8. abacbc ⇒ ac [7]
9. (cba)2 ⇒ ac [5]
10. cbacbc ⇒ c2 [15]
# ab:abaaabab=aab ac/b abaaaba=c morph:7/0
aac=cc
cac=acc
aab=cb
cab=acb
ccba=abcc
ccbc=abacc
abacba=c
abacbc=ac
cbacba=ac
cbacbc=cc