#2298 ⟨a, b | aaa=1, ababab=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. b(ab)2 ⇒ a2 [3]
# ab:aaa=1,ababab=1 ab - -
aaa=1
babab=aa

Isomorphic instances

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

6 total

Σ#PresentationMapping
107811⟨a, b | aaa=1, babab=aa⟩φ(a) = a, φ(b) = b
1113819⟨a, b | aaaa=a, ababab=1⟩φ(a) = a, φ(b) = b
1113958⟨a, b | aaab=b, ababab=1⟩φ(a) = a, φ(b) = b
1113979⟨a, b | aaab=b, bababa=1⟩φ(a) = a, φ(b) = b
1121688⟨a, b | aaa=1, aababab=a⟩φ(a) = a, φ(b) = b
1121722⟨a, b | aaa=1, abababa=a⟩φ(a) = a, φ(b) = b