#6917 ⟨a, b | ba=ab, aaabbb=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. a3b3 ⇒ 1 [2]
# ab:ba=ab,aaabbb=1 ab - -
ba=ab
aaabbb=1

Isomorphic instances

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

6 total

Σ#PresentationMapping
106920⟨a, b | ba=ab, aababb=1⟩φ(a) = a, φ(b) = b
106922⟨a, b | ba=ab, aabbab=1⟩φ(a) = a, φ(b) = b
106923⟨a, b | ba=ab, aabbba=1⟩φ(a) = a, φ(b) = b
106926⟨a, b | ba=ab, ababab=1⟩φ(a) = a, φ(b) = b
106927⟨a, b | ba=ab, ababba=1⟩φ(a) = a, φ(b) = b
106928⟨a, b | ba=ab, abbaab=1⟩φ(a) = a, φ(b) = b