#28 ⟨a, b | aaa=1, bbb=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. a3 ⇒ 1 [1]
2. b3 ⇒ 1 [2]
# ab:aaa=1,bbb=1 ab - -
aaa=1
bbb=1

Isomorphic instances

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

22 total

Σ#PresentationMapping
8748⟨a, b | aaa=1, abbb=a⟩φ(a) = a, φ(b) = b
92287⟨a, b | aaa=1, aaabbb=1⟩φ(a) = a, φ(b) = b
92293⟨a, b | aaa=1, aabbba=1⟩φ(a) = a, φ(b) = b
92307⟨a, b | aaa=1, baaabb=1⟩φ(a) = a, φ(b) = b
92700⟨a, b | aaa=1, bbb=aaa⟩φ(a) = a, φ(b) = b
107778⟨a, b | aaa=1, aabbb=aa⟩φ(a) = a, φ(b) = b
107797⟨a, b | aaa=1, abbba=aa⟩φ(a) = a, φ(b) = b
1113808⟨a, b | aaaa=a, aaabbb=1⟩φ(a) = a, φ(b) = b
1113814⟨a, b | aaaa=a, aabbba=1⟩φ(a) = a, φ(b) = b
1113828⟨a, b | aaaa=a, baaabb=1⟩φ(a) = a, φ(b) = b
1113944⟨a, b | aaab=b, aaabbb=1⟩φ(a) = a, φ(b) = b
1113951⟨a, b | aaab=b, aabbba=1⟩φ(a) = a, φ(b) = b
1113965⟨a, b | aaab=b, abbbaa=1⟩φ(a) = a, φ(b) = b
1113972⟨a, b | aaab=b, baaabb=1⟩φ(a) = a, φ(b) = b
1113986⟨a, b | aaab=b, bbaaab=1⟩φ(a) = a, φ(b) = b
1113993⟨a, b | aaab=b, bbbaaa=1⟩φ(a) = a, φ(b) = b
1121662⟨a, b | aaa=1, aaaabbb=a⟩φ(a) = a, φ(b) = b
1121676⟨a, b | aaa=1, aaabbba=a⟩φ(a) = a, φ(b) = b
1121700⟨a, b | aaa=1, aabbbaa=a⟩φ(a) = a, φ(b) = b
1121712⟨a, b | aaa=1, abaaabb=a⟩φ(a) = a, φ(b) = b
1121732⟨a, b | aaa=1, abbaaab=a⟩φ(a) = a, φ(b) = b
1123283⟨a, b | aaa=1, abbb=aaaa⟩φ(a) = a, φ(b) = b