#141 ⟨a, b | bab=a, bbb=1⟩

Up:Monoid enumeration
Prev:#134 ⟨a, b | aba=a, bbb=1⟩
Next:#151 ⟨a, b | ba=ab, aaa=1⟩

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. b3 ⇒ 1 [2]
2. ba ⇒ ab2 [3]
# ab:bab=a,bbb=1 b/a - -
bbb=1
ba=abb

Isomorphic instances

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

11 total

Σ#PresentationMapping
8448⟨a, b | abb=ba, bbb=1⟩φ(a) = a, φ(b) = b
92425⟨a, b | aaa=1, aabaa=b⟩φ(a) = b, φ(b) = a
92568⟨a, b | aaa=1, aaba=ab⟩φ(a) = b, φ(b) = a
107485⟨a, b | aaa=1, aaaaba=b⟩φ(a) = b, φ(b) = a
108032⟨a, b | aaa=1, aaab=aba⟩φ(a) = b, φ(b) = a
108042⟨a, b | aaa=1, aaba=baa⟩φ(a) = b, φ(b) = a
1122197⟨a, b | aaa=1, aaaaab=ba⟩φ(a) = b, φ(b) = a
1122208⟨a, b | aaa=1, aaabaa=ab⟩φ(a) = b, φ(b) = a
1122730⟨a, b | aaa=1, aaaab=baa⟩φ(a) = b, φ(b) = a
1122735⟨a, b | aaa=1, aaaba=aab⟩φ(a) = b, φ(b) = a
1122752⟨a, b | aaa=1, aabaa=aba⟩φ(a) = b, φ(b) = a