#6171 ⟨a, b, c | aa=1, abbccb=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. ab2c2 ⇒ bc2ba [6]
3. abc2b ⇒ b2c2a [5]
4. c2bab ⇒ bc2ba [9]
5. b2c2b ⇒ a [3]
6. cbab2 ⇒ bab2c [15]
7. c2b3c2 ⇒ b(c2ba)2 [11]
8. ab2cbc2b ⇒ bc(cba)2ba [13]
9. c2b3cbc2b ⇒ b(c2ba)2c(ba)2 [16]
# abc:aa=1,abbccb=1 ac/b - -
aa=1
abbcc=bccba
abccb=bbcca
ccbab=bccba
bbccb=a
cbabb=babbc
ccbbbcc=bccbaccba
abbcbccb=bccbacbaba
ccbbbcbccb=bccbaccbacbaba

Isomorphic instances

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

10 total

Σ#PresentationMapping
86189⟨a, b, c | aa=1, abccbb=1⟩φ(a) = bccbabccbababbcbabbcbccba, φ(b) = b, φ(c) = c
86191⟨a, b, c | aa=1, abcccb=1⟩φ(a) = babbcbccbabccbabccbababbc, φ(b) = c, φ(c) = b
86218⟨a, b, c | aa=1, babccb=1⟩φ(a) = bccbabccbababbcbabbcbccba, φ(b) = b, φ(c) = c
86230⟨a, b, c | aa=1, baccbb=1⟩φ(a) = bccbabccbabccbababbcbabbc, φ(b) = b, φ(c) = c
86232⟨a, b, c | aa=1, bacccb=1⟩φ(a) = babbcbabbcbccbabccbabccba, φ(b) = c, φ(c) = b
86242⟨a, b, c | aa=1, bbaccb=1⟩φ(a) = bccbabccbabccbababbcbabbc, φ(b) = b, φ(c) = c
86254⟨a, b, c | aa=1, bbcacb=1⟩φ(a) = babbcbccbabccbabccbababbc, φ(b) = b, φ(c) = c
86266⟨a, b, c | aa=1, bcaccb=1⟩φ(a) = bccbababbcbabbcbccbabccba, φ(b) = c, φ(c) = b
86763⟨a, b, c | aa=1, bbccb=a⟩φ(a) = bccbabccbababbcbabbcbccba, φ(b) = bccba, φ(c) = babbc
86777⟨a, b, c | aa=1, bcccb=a⟩φ(a) = babbcbccbabccbabccbababbc, φ(b) = babbc, φ(c) = bccba