#139 ⟨a, b, c | aa=b, ac=a⟩

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. ac ⇒ a [2]
2. b ⇒ a2 [1]
# abc:aa=b,ac=a ac/b - -
ac=a
b=aa

Isomorphic instances

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

25 total

Σ#PresentationMapping
6150⟨a, b, c | ab=a, ba=c⟩φ(a) = a, φ(b) = c, φ(c) = ca
7943⟨a, b, c | ab=a, aaa=c⟩φ(a) = a, φ(b) = c, φ(c) = aaa
7944⟨a, b, c | ab=a, aab=c⟩φ(a) = a, φ(b) = c, φ(c) = aa
7948⟨a, b, c | ab=a, aba=c⟩φ(a) = a, φ(b) = c, φ(c) = aa
7949⟨a, b, c | ab=a, abb=c⟩φ(a) = a, φ(b) = c, φ(c) = a
7962⟨a, b, c | ab=a, baa=c⟩φ(a) = a, φ(b) = c, φ(c) = caa
7963⟨a, b, c | ab=a, bab=c⟩φ(a) = a, φ(b) = c, φ(c) = ca
7967⟨a, b, c | ab=a, bba=c⟩φ(a) = a, φ(b) = c, φ(c) = cca
7968⟨a, b, c | ab=a, bbb=c⟩φ(a) = a, φ(b) = c, φ(c) = ccc
85274⟨a, b, c | ab=a, aaaa=c⟩φ(a) = a, φ(b) = c, φ(c) = aaaa
85275⟨a, b, c | ab=a, aaab=c⟩φ(a) = a, φ(b) = c, φ(c) = aaa
85279⟨a, b, c | ab=a, aaba=c⟩φ(a) = a, φ(b) = c, φ(c) = aaa
85280⟨a, b, c | ab=a, aabb=c⟩φ(a) = a, φ(b) = c, φ(c) = aa
85293⟨a, b, c | ab=a, abaa=c⟩φ(a) = a, φ(b) = c, φ(c) = aaa
85294⟨a, b, c | ab=a, abab=c⟩φ(a) = a, φ(b) = c, φ(c) = aa
85298⟨a, b, c | ab=a, abba=c⟩φ(a) = a, φ(b) = c, φ(c) = aa
85299⟨a, b, c | ab=a, abbb=c⟩φ(a) = a, φ(b) = c, φ(c) = a
85339⟨a, b, c | ab=a, baaa=c⟩φ(a) = a, φ(b) = c, φ(c) = caaa
85340⟨a, b, c | ab=a, baab=c⟩φ(a) = a, φ(b) = c, φ(c) = caa
85344⟨a, b, c | ab=a, baba=c⟩φ(a) = a, φ(b) = c, φ(c) = caa
85345⟨a, b, c | ab=a, babb=c⟩φ(a) = a, φ(b) = c, φ(c) = ca
85358⟨a, b, c | ab=a, bbaa=c⟩φ(a) = a, φ(b) = c, φ(c) = ccaa
85359⟨a, b, c | ab=a, bbab=c⟩φ(a) = a, φ(b) = c, φ(c) = cca
85363⟨a, b, c | ab=a, bbba=c⟩φ(a) = a, φ(b) = c, φ(c) = ccca
85364⟨a, b, c | ab=a, bbbb=c⟩φ(a) = a, φ(b) = c, φ(c) = cccc