#175 ⟨a, b, c | aa=1, bccb=1⟩

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Contents

  1. Properties
  2. Rewriting system
  3. Isomorphic instances

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. a2 ⇒ 1 [1]
2. b2d ⇒ db2 [13]
3. cb ⇒ d [3]
4. b2c ⇒ db [10]
5. dbd ⇒ b [12]
6. dbc ⇒ 1 [11]
7. cdb ⇒ 1 [8]
8. bcd ⇒ 1 [4]
9. bc2 ⇒ cd [6]
10. dcd ⇒ c [5]
11. cd2 ⇒ bdc2 [14]
12. c2d ⇒ dc2 [7]
# abc:aa=1,bccb=1 ab/dc cb=d morph:2/0
aa=1
bbd=dbb
cb=d
bbc=db
dbd=b
dbc=1
cdb=1
bcd=1
bcc=cd
dcd=c
cdd=bdcc
ccd=dcc

Isomorphic instances

The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.

8 total

Σ#PresentationMapping
82449⟨a, b, c | aab=b, bccb=1⟩φ(a) = a, φ(b) = b, φ(c) = c
82465⟨a, b, c | aab=b, cbbc=1⟩φ(a) = a, φ(b) = b, φ(c) = c
86136⟨a, b, c | aa=1, aabccb=1⟩φ(a) = a, φ(b) = b, φ(c) = c
86188⟨a, b, c | aa=1, abccba=1⟩φ(a) = a, φ(b) = b, φ(c) = c
86205⟨a, b, c | aa=1, baaccb=1⟩φ(a) = a, φ(b) = b, φ(c) = c
86262⟨a, b, c | aa=1, bcaacb=1⟩φ(a) = a, φ(b) = b, φ(c) = c
86690⟨a, b, c | aa=1, abccb=a⟩φ(a) = a, φ(b) = b, φ(c) = c
87271⟨a, b, c | aa=1, bccb=aa⟩φ(a) = a, φ(b) = b, φ(c) = c