#55 ⟨a, b, c | aaa=1, abc=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. (bc)3 ⇒ 1 [6]
2. a ⇒ (bc)2 [5]
# abc:aaa=1,abc=1 bc/a - -
bcbcbc=1
a=bcbc

Isomorphic instances

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

22 total

Σ#PresentationMapping
6133⟨a, b, c | ab=c, ccc=1⟩φ(a) = b, φ(b) = c, φ(c) = bc
7495⟨a, b, c | bb=ac, acb=1⟩φ(a) = b, φ(b) = bcbc, φ(c) = c
7499⟨a, b, c | bb=ac, bbb=1⟩φ(a) = b, φ(b) = bcbc, φ(c) = c
7565⟨a, b, c | aaa=1, aabc=1⟩φ(a) = bc, φ(b) = b, φ(c) = c
7568⟨a, b, c | aaa=1, abca=1⟩φ(a) = bc, φ(b) = b, φ(c) = c
7856⟨a, b, c | ab=c, abcc=1⟩φ(a) = b, φ(b) = c, φ(c) = bc
7877⟨a, b, c | ab=c, bcca=1⟩φ(a) = c, φ(b) = b, φ(c) = cb
7880⟨a, b, c | ab=c, cabc=1⟩φ(a) = b, φ(b) = c, φ(c) = bc
82028⟨a, b, c | abc=cc, ccc=1⟩φ(a) = b, φ(b) = c, φ(c) = bc
82644⟨a, b, c | aba=c, abcb=1⟩φ(a) = b, φ(b) = c, φ(c) = bcb
82656⟨a, b, c | aba=c, babc=1⟩φ(a) = c, φ(b) = b, φ(c) = cbc
84108⟨a, b, c | aaa=1, aabc=a⟩φ(a) = bcbc, φ(b) = b, φ(c) = c
84120⟨a, b, c | aaa=1, abca=a⟩φ(a) = bcbc, φ(b) = b, φ(c) = c
84481⟨a, b, c | abc=1, aaaa=a⟩φ(a) = bcbc, φ(b) = b, φ(c) = c
84485⟨a, b, c | abc=1, aaab=b⟩φ(a) = bcbc, φ(b) = b, φ(c) = c
84512⟨a, b, c | abc=1, abab=c⟩φ(a) = b, φ(b) = c, φ(c) = bcbc
84594⟨a, b, c | abc=1, caaa=c⟩φ(a) = bcbc, φ(b) = b, φ(c) = c
84599⟨a, b, c | abc=1, caca=b⟩φ(a) = b, φ(b) = cbcb, φ(c) = c
85013⟨a, b, c | ab=c, ababc=1⟩φ(a) = b, φ(b) = c, φ(c) = bc
85025⟨a, b, c | ab=c, abcab=1⟩φ(a) = b, φ(b) = c, φ(c) = bc
85061⟨a, b, c | ab=c, babca=1⟩φ(a) = c, φ(b) = b, φ(c) = cb
87091⟨a, b, c | ab=1, cacac=b⟩φ(a) = b, φ(b) = cbcbc, φ(c) = c