#3125 ⟨a, b, c | ab=aa, cbbc=1⟩

Up:Monoid enumeration
Prev:#3124 ⟨a, b, c | ab=aa, cbbb=1⟩
Next:#3127 ⟨a, b, c | ab=aa, cbcb=1⟩

Contents

  1. Properties
  2. Rewriting system

Properties

Rewriting system

Format:
Word:
Enter a word above to compute its normal form. Tips:
  • Lowercase letters stand for generators.
  • Spaces are ignored.
  • Numbers repeat the previous letter, e.g. b90.
Strategy:
Result: 1 
1
#RuleProof
1. ab ⇒ a2 [1]
2. db2 ⇒ b2d [8]
3. bc ⇒ d [3]
4. a2c ⇒ ad [6]
5. cb2 ⇒ bd [7]
6. dbd ⇒ b [5]
7. cbd ⇒ 1 [4]
8. bdc ⇒ 1 [9]
9. a2dc ⇒ a [10]
10. dcb ⇒ 1 [13]
11. c2b ⇒ dc [12]
12. dcd ⇒ c [14]
13. d2c ⇒ c2db [16]
14. dc2 ⇒ c2d [15]
# abc:ab=aa,cbbc=1 reversed:ab/dc bc=d morph:2/0
ab=aa
dbb=bbd
bc=d
aac=ad
cbb=bd
dbd=b
cbd=1
bdc=1
aadc=a
dcb=1
ccb=dc
dcd=c
ddc=ccdb
dcc=ccd