#2461 ⟨a, b | aaabba=baaa⟩

Up:Monoids with two generators and one relation
Prev:#2460 ⟨a, b | aaabba=abbb⟩
Next:#2462 ⟨a, b | aaabba=baab⟩

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. a3f2 ⇒ fa2 [24]
2. a3fe ⇒ f [15]
3. ef ⇒ fafe [16]
4. ea2 ⇒ f [5]
5. eaf ⇒ fa2fe [17]
6. df ⇒ a(a2f)2e2 [23]
7. da2 ⇒ a3e [13]
8. daf ⇒ fa2e [14]
9. dae ⇒ ead [8]
10. cf ⇒ a3fa2e2 [21]
11. ca2 ⇒ a3d [12]
12. caf ⇒ a6fafe2 [22]
13. bf ⇒ a6fa2e3 [25]
14. baf ⇒ a9fafe3 [26]
15. ba3 ⇒ a3c [6]
16. ba2f ⇒ a9fa2fe3 [27]
17. dad ⇒ e [4]
18. dc ⇒ cd [7]
19. dace ⇒ ecad [11]
20. c2 ⇒ d [3]
21. b2a ⇒ c [2]
22. dacd ⇒ ec [9]
# ab:aaabba=baaa reversed:af/e/dcb bba=c,cc=d,dad=e,eaa=f morph:3/2,2/2,3/2,3/0
aaaff=faa
aaafe=f
ef=fafe
eaa=f
eaf=faafe
df=aaafaafee
daa=aaae
daf=faae
dae=ead
cf=aaafaaee
caa=aaad
caf=aaaaaafafee
bf=aaaaaafaaeee
baf=aaaaaaaaafafeee
baaa=aaac
baaf=aaaaaaaaafaafeee
dad=e
dc=cd
dace=ecad
cc=d
bba=c
dacd=ec