#750 ⟨a, b | aaa=1, baab=a⟩

Up:Monoid enumeration
Prev:#736 ⟨a, b | aaa=1, aaaa=a⟩
Next:#751 ⟨a, b | aaa=1, baab=b⟩

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]
2. ba2b ⇒ a [2]
# ab:aaa=1,baab=a ab - -
aaa=1
baab=a

Isomorphic instances

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

14 total

Σ#PresentationMapping
92288⟨a, b | aaa=1, aabaab=1⟩φ(a) = a, φ(b) = b
92296⟨a, b | aaa=1, abaaba=1⟩φ(a) = a, φ(b) = b
107782⟨a, b | aaa=1, abaab=aa⟩φ(a) = a, φ(b) = b
1113809⟨a, b | aaaa=a, aabaab=1⟩φ(a) = a, φ(b) = b
1113817⟨a, b | aaaa=a, abaaba=1⟩φ(a) = a, φ(b) = b
1113946⟨a, b | aaab=b, aabaab=1⟩φ(a) = a, φ(b) = b
1113955⟨a, b | aaab=b, abaaba=1⟩φ(a) = a, φ(b) = b
1113973⟨a, b | aaab=b, baabaa=1⟩φ(a) = a, φ(b) = b
1114315⟨a, b | abba=b, abbabb=1⟩φ(a) = b, φ(b) = a
1114324⟨a, b | abba=b, babbab=1⟩φ(a) = b, φ(b) = a
1121666⟨a, b | aaa=1, aaabaab=a⟩φ(a) = a, φ(b) = b
1121682⟨a, b | aaa=1, aabaaba=a⟩φ(a) = a, φ(b) = b
1121752⟨a, b | aaa=1, baaaaab=a⟩φ(a) = a, φ(b) = b
1123294⟨a, b | aaa=1, baab=aaaa⟩φ(a) = a, φ(b) = b