#936 ⟨a, b | ab=a, baaa=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. ab ⇒ a [1]
2. ba ⇒ a [6]
3. a3 ⇒ a [5]
# ab:ab=a,baaa=a ab - -
ab=a
ba=a
aaa=a

Isomorphic instances

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

55 total

Σ#PresentationMapping
92970⟨a, b | ab=a, baaab=a⟩φ(a) = a, φ(b) = b
92972⟨a, b | ab=a, baaba=a⟩φ(a) = a, φ(b) = b
92976⟨a, b | ab=a, babaa=a⟩φ(a) = a, φ(b) = b
93105⟨a, b | ab=a, baaa=ab⟩φ(a) = a, φ(b) = b
105110⟨a, b | aab=aa, baaa=a⟩φ(a) = a, φ(b) = b
105173⟨a, b | aab=ba, abbb=b⟩φ(a) = b, φ(b) = a
105257⟨a, b | aba=ab, abbb=b⟩φ(a) = b, φ(b) = a
108782⟨a, b | ab=a, baaabb=a⟩φ(a) = a, φ(b) = b
108786⟨a, b | ab=a, baabab=a⟩φ(a) = a, φ(b) = b
108788⟨a, b | ab=a, baabba=a⟩φ(a) = a, φ(b) = b
108794⟨a, b | ab=a, babaab=a⟩φ(a) = a, φ(b) = b
108796⟨a, b | ab=a, bababa=a⟩φ(a) = a, φ(b) = b
108800⟨a, b | ab=a, babbaa=a⟩φ(a) = a, φ(b) = b
109053⟨a, b | ab=a, baaab=ab⟩φ(a) = a, φ(b) = b
109057⟨a, b | ab=a, baaba=ab⟩φ(a) = a, φ(b) = b
109065⟨a, b | ab=a, babaa=ab⟩φ(a) = a, φ(b) = b
109323⟨a, b | ab=a, baaa=abb⟩φ(a) = a, φ(b) = b
1112270⟨a, b | aaab=ba, aaba=a⟩φ(a) = a, φ(b) = b
1112274⟨a, b | aaab=ba, abaa=a⟩φ(a) = a, φ(b) = b
1112282⟨a, b | aaab=ba, baaa=a⟩φ(a) = a, φ(b) = b
1112362⟨a, b | aaba=ab, baaa=a⟩φ(a) = a, φ(b) = b
1112492⟨a, b | abaa=ab, baaa=a⟩φ(a) = a, φ(b) = b
1114443⟨a, b | aaab=a, baaab=a⟩φ(a) = a, φ(b) = b
1114445⟨a, b | aaab=a, baaba=a⟩φ(a) = a, φ(b) = b
1114449⟨a, b | aaab=a, babaa=a⟩φ(a) = a, φ(b) = b
1114571⟨a, b | aaba=a, baaab=a⟩φ(a) = a, φ(b) = b
1115579⟨a, b | aab=aa, baaab=a⟩φ(a) = a, φ(b) = b
1115581⟨a, b | aab=aa, baaba=a⟩φ(a) = a, φ(b) = b
1115585⟨a, b | aab=aa, babaa=a⟩φ(a) = a, φ(b) = b
1115638⟨a, b | aab=ab, abbba=b⟩φ(a) = b, φ(b) = a
1115700⟨a, b | aab=ba, abbab=b⟩φ(a) = b, φ(b) = a
1115829⟨a, b | aba=aa, baaab=a⟩φ(a) = a, φ(b) = b
1115864⟨a, b | aba=ab, ababb=b⟩φ(a) = b, φ(b) = a
1115868⟨a, b | aba=ab, abbab=b⟩φ(a) = b, φ(b) = a
1115870⟨a, b | aba=ab, abbba=b⟩φ(a) = b, φ(b) = a
1124474⟨a, b | ab=a, baaabbb=a⟩φ(a) = a, φ(b) = b
1124482⟨a, b | ab=a, baababb=a⟩φ(a) = a, φ(b) = b
1124486⟨a, b | ab=a, baabbab=a⟩φ(a) = a, φ(b) = b
1124488⟨a, b | ab=a, baabbba=a⟩φ(a) = a, φ(b) = b
1124498⟨a, b | ab=a, babaabb=a⟩φ(a) = a, φ(b) = b
1124502⟨a, b | ab=a, bababab=a⟩φ(a) = a, φ(b) = b
1124504⟨a, b | ab=a, bababba=a⟩φ(a) = a, φ(b) = b
1124510⟨a, b | ab=a, babbaab=a⟩φ(a) = a, φ(b) = b
1124512⟨a, b | ab=a, babbaba=a⟩φ(a) = a, φ(b) = b
1124516⟨a, b | ab=a, babbbaa=a⟩φ(a) = a, φ(b) = b
1125001⟨a, b | ab=a, baaabb=ab⟩φ(a) = a, φ(b) = b
1125009⟨a, b | ab=a, baabab=ab⟩φ(a) = a, φ(b) = b
1125013⟨a, b | ab=a, baabba=ab⟩φ(a) = a, φ(b) = b
1125025⟨a, b | ab=a, babaab=ab⟩φ(a) = a, φ(b) = b
1125029⟨a, b | ab=a, bababa=ab⟩φ(a) = a, φ(b) = b
1125037⟨a, b | ab=a, babbaa=ab⟩φ(a) = a, φ(b) = b
1125543⟨a, b | ab=a, baaab=abb⟩φ(a) = a, φ(b) = b
1125551⟨a, b | ab=a, baaba=abb⟩φ(a) = a, φ(b) = b
1125567⟨a, b | ab=a, babaa=abb⟩φ(a) = a, φ(b) = b
1125827⟨a, b | ab=a, baaa=abbb⟩φ(a) = a, φ(b) = b