#151 ⟨a, b | ba=ab, aaa=1⟩

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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. ba ⇒ ab [1]
2. a3 ⇒ 1 [2]
# ab:ba=ab,aaa=1 ab - -
ba=ab
aaa=1

Isomorphic instances

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

11 total

Σ#PresentationMapping
8741⟨a, b | aaa=1, aaba=b⟩φ(a) = a, φ(b) = b
91311⟨a, b | bab=abb, bbb=1⟩φ(a) = b, φ(b) = a
91313⟨a, b | bba=abb, bbb=1⟩φ(a) = b, φ(b) = a
107757⟨a, b | aaa=1, aaaab=ba⟩φ(a) = a, φ(b) = b
107760⟨a, b | aaa=1, aaaba=ab⟩φ(a) = a, φ(b) = b
107768⟨a, b | aaa=1, aabaa=ab⟩φ(a) = a, φ(b) = b
1121653⟨a, b | aaa=1, aaaaaba=b⟩φ(a) = a, φ(b) = b
1121657⟨a, b | aaa=1, aaaabaa=b⟩φ(a) = a, φ(b) = b
1123266⟨a, b | aaa=1, aaba=aaab⟩φ(a) = a, φ(b) = b
1123270⟨a, b | aaa=1, abaa=aaab⟩φ(a) = a, φ(b) = b
1123271⟨a, b | aaa=1, abaa=aaba⟩φ(a) = a, φ(b) = b