#23 ⟨a, b | ba=ab, bb=1⟩

Up:Monoid enumeration
Prev:#22 ⟨a, b | ab=aa, bb=1⟩
Next:#26 ⟨a, b | aaa=1, abb=1⟩

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. b2 ⇒ 1 [2]
# ab:ba=ab,bb=1 ab - -
ba=ab
bb=1

Isomorphic instances

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

17 total

Σ#PresentationMapping
689⟨a, b | aa=1, aba=b⟩φ(a) = b, φ(b) = a
81101⟨a, b | aa=1, aaaba=b⟩φ(a) = b, φ(b) = a
81173⟨a, b | aa=1, aaab=ba⟩φ(a) = b, φ(b) = a
81176⟨a, b | aa=1, aaba=ab⟩φ(a) = b, φ(b) = a
81242⟨a, b | aa=1, aba=aab⟩φ(a) = b, φ(b) = a
109661⟨a, b | aa=1, aaaaaba=b⟩φ(a) = b, φ(b) = a
109673⟨a, b | aa=1, aaabaaa=b⟩φ(a) = b, φ(b) = a
109933⟨a, b | aa=1, aaaaab=ba⟩φ(a) = b, φ(b) = a
109936⟨a, b | aa=1, aaaaba=ab⟩φ(a) = b, φ(b) = a
109945⟨a, b | aa=1, aaabaa=ba⟩φ(a) = b, φ(b) = a
1010208⟨a, b | aa=1, aaaab=aba⟩φ(a) = b, φ(b) = a
1010215⟨a, b | aa=1, aaaba=aab⟩φ(a) = b, φ(b) = a
1010218⟨a, b | aa=1, aaaba=baa⟩φ(a) = b, φ(b) = a
1010232⟨a, b | aa=1, aabaa=aba⟩φ(a) = b, φ(b) = a
1010474⟨a, b | aa=1, aaba=aaab⟩φ(a) = b, φ(b) = a
1010479⟨a, b | aa=1, abaa=aaba⟩φ(a) = b, φ(b) = a
1010498⟨a, b | aa=1, baaa=aaab⟩φ(a) = b, φ(b) = a