#827 ⟨a, b, c | ab=a, cbbc=1⟩

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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 ⇒ a [1]
2. db2 ⇒ b2d [8]
3. ac ⇒ ad [5]
4. bc ⇒ d [3]
5. cb2 ⇒ bd [7]
6. dbd ⇒ b [6]
7. cbd ⇒ 1 [4]
8. adc ⇒ a [10]
9. bdc ⇒ 1 [9]
10. dcb ⇒ 1 [13]
11. c2b ⇒ dc [12]
12. dcd ⇒ c [14]
13. d2c ⇒ c2db [16]
14. dc2 ⇒ c2d [15]
# abc:ab=a,cbbc=1 reversed:ab/dc bc=d morph:2/0
ab=a
dbb=bbd
ac=ad
bc=d
cbb=bd
dbd=b
cbd=1
adc=a
bdc=1
dcb=1
ccb=dc
dcd=c
ddc=ccdb
dcc=ccd