#3177 ⟨a, b, c | ac=ab, bccb=1⟩

Up:Monoid enumeration
Prev:#3175 ⟨a, b, c | ac=ab, bcbc=1⟩
Next:#3178 ⟨a, b, c | ac=ab, bccc=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. ad ⇒ ab3 [4]
2. abd ⇒ a [8]
3. b2d ⇒ db2 [12]
4. cb2 ⇒ d [3]
5. ac ⇒ ab [1]
6. b2c ⇒ d [11]
7. d2 ⇒ b2 [10]
8. dc ⇒ 1 [9]
9. cd ⇒ 1 [6]
10. cbd ⇒ dbc [13]
11. bc2 ⇒ c2b [5]
# abc:ac=ab,bccb=1 ab/dc cbb=d morph:3/2
ad=abbb
abd=a
bbd=dbb
cbb=d
ac=ab
bbc=d
dd=bb
dc=1
cd=1
cbd=dbc
bcc=ccb