#1592 ⟨a, b | aaa=ab, baa=a⟩

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Contents

  1. Properties
  2. Commutative structure
  3. Staircase diagram
  4. Rewriting system
  5. Isomorphic instances

Properties

Commutative structure

Staircase diagram

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. ab3 ⇒ a [6]
2. ba ⇒ ab [7]
3. a2 ⇒ ab2 [8]
# ab:aaa=ab,baa=a b/a - -
abbb=a
ba=ab
aa=abb

Isomorphic instances

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

39 total

Σ#PresentationMapping
91679⟨a, b | aba=bb, abb=b⟩φ(a) = b, φ(b) = a
91683⟨a, b | aba=bb, bab=b⟩φ(a) = b, φ(b) = a
92042⟨a, b | aab=a, babb=a⟩φ(a) = a, φ(b) = b
105279⟨a, b | aba=bb, aaba=b⟩φ(a) = b, φ(b) = a
1112464⟨a, b | aabb=ab, babb=a⟩φ(a) = a, φ(b) = b
1112470⟨a, b | aabb=ba, abaa=b⟩φ(a) = b, φ(b) = a
1112539⟨a, b | abab=ba, babb=a⟩φ(a) = a, φ(b) = b
1112542⟨a, b | abab=ba, bbab=a⟩φ(a) = a, φ(b) = b
1112576⟨a, b | abba=ab, babb=a⟩φ(a) = a, φ(b) = b
1112620⟨a, b | baab=ab, bbab=a⟩φ(a) = a, φ(b) = b
1118896⟨a, b | aab=a, baaaaa=a⟩φ(a) = a, φ(b) = b
1118910⟨a, b | aab=a, baabbb=a⟩φ(a) = a, φ(b) = b
1118918⟨a, b | aab=a, bababb=a⟩φ(a) = a, φ(b) = b
1118922⟨a, b | aab=a, babbab=a⟩φ(a) = a, φ(b) = b
1118924⟨a, b | aab=a, babbba=a⟩φ(a) = a, φ(b) = b
1119150⟨a, b | aba=a, babbab=a⟩φ(a) = a, φ(b) = b
1119382⟨a, b | aab=a, aaaab=ba⟩φ(a) = a, φ(b) = b
1119386⟨a, b | aab=a, aaaba=ba⟩φ(a) = a, φ(b) = b
1119394⟨a, b | aab=a, aabaa=ba⟩φ(a) = a, φ(b) = b
1119410⟨a, b | aab=a, abaaa=ba⟩φ(a) = a, φ(b) = b
1119438⟨a, b | aab=a, abbbb=ba⟩φ(a) = a, φ(b) = b
1119441⟨a, b | aab=a, baaaa=ab⟩φ(a) = a, φ(b) = b
1119452⟨a, b | aab=a, baabb=aa⟩φ(a) = a, φ(b) = b
1119460⟨a, b | aab=a, babab=aa⟩φ(a) = a, φ(b) = b
1119464⟨a, b | aab=a, babba=aa⟩φ(a) = a, φ(b) = b
1119469⟨a, b | aab=a, babbb=ab⟩φ(a) = a, φ(b) = b
1119637⟨a, b | aba=a, aaaab=ba⟩φ(a) = a, φ(b) = b
1119691⟨a, b | aba=a, babab=aa⟩φ(a) = a, φ(b) = b
1119924⟨a, b | aab=a, aaaa=baa⟩φ(a) = a, φ(b) = b
1119933⟨a, b | aab=a, aaab=bab⟩φ(a) = a, φ(b) = b
1119941⟨a, b | aab=a, aaba=bab⟩φ(a) = a, φ(b) = b
1119957⟨a, b | aab=a, abaa=bab⟩φ(a) = a, φ(b) = b
1119980⟨a, b | aab=a, abbb=baa⟩φ(a) = a, φ(b) = b
1119987⟨a, b | aab=a, baaa=abb⟩φ(a) = a, φ(b) = b
1119992⟨a, b | aab=a, baab=aaa⟩φ(a) = a, φ(b) = b
1120000⟨a, b | aab=a, baba=aaa⟩φ(a) = a, φ(b) = b
1120009⟨a, b | aab=a, babb=aab⟩φ(a) = a, φ(b) = b
1120010⟨a, b | aab=a, babb=aba⟩φ(a) = a, φ(b) = b
1120195⟨a, b | aba=a, aaba=bab⟩φ(a) = a, φ(b) = b