#736 ⟨a, b | aaa=1, aaaa=a⟩

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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]
# ab:aaa=1,aaaa=a ab - -
aaa=1

Isomorphic instances

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

12 total

Σ#PresentationMapping
8739⟨a, b | aaa=1, aaab=b⟩φ(a) = a, φ(b) = 1
92280⟨a, b | aaa=1, aaaaaa=1⟩φ(a) = a, φ(b) = 1
107752⟨a, b | aaa=1, aaaaa=aa⟩φ(a) = a, φ(b) = 1
107756⟨a, b | aaa=1, aaaab=ab⟩φ(a) = a, φ(b) = 1
107761⟨a, b | aaa=1, aaaba=ba⟩φ(a) = a, φ(b) = 1
107766⟨a, b | aaa=1, aaabb=bb⟩φ(a) = a, φ(b) = 1
107806⟨a, b | aaa=1, baaab=bb⟩φ(a) = a, φ(b) = 1
1113801⟨a, b | aaaa=a, aaaaaa=1⟩φ(a) = a, φ(b) = 1
1121648⟨a, b | aaa=1, aaaaaaa=a⟩φ(a) = a, φ(b) = 1
1121651⟨a, b | aaa=1, aaaaaab=b⟩φ(a) = a, φ(b) = 1
1121665⟨a, b | aaa=1, aaabaaa=b⟩φ(a) = a, φ(b) = 1
1123290⟨a, b | aaa=1, baaa=aaab⟩φ(a) = a, φ(b) = 1