#2878 ⟨a, b | aa=a, abbab=a⟩

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Contents

  1. Properties
  2. Rewriting system
  3. Isomorphic instances
  4. Anti-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. a2 ⇒ a [1]
2. aba ⇒ ab [5]
3. ab2a ⇒ ab2 [7]
4. ab3 ⇒ a [6]
# ab:aa=a,abbab=a ab - -
aa=a
aba=ab
abba=abb
abbb=a

Isomorphic instances

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

21 total

Σ#PresentationMapping
105256⟨a, b | aba=ab, abbb=a⟩φ(a) = a, φ(b) = b
108592⟨a, b | aa=a, aabbab=a⟩φ(a) = a, φ(b) = b
108604⟨a, b | aa=a, ababab=a⟩φ(a) = a, φ(b) = b
108610⟨a, b | aa=a, abbaab=a⟩φ(a) = a, φ(b) = b
108881⟨a, b | aa=a, abbab=aa⟩φ(a) = a, φ(b) = b
1115423⟨a, b | aaa=aa, abbab=a⟩φ(a) = a, φ(b) = b
1115635⟨a, b | aab=ab, abbab=a⟩φ(a) = a, φ(b) = b
1115855⟨a, b | aba=ab, aabbb=a⟩φ(a) = a, φ(b) = b
1115863⟨a, b | aba=ab, ababb=a⟩φ(a) = a, φ(b) = b
1115867⟨a, b | aba=ab, abbab=a⟩φ(a) = a, φ(b) = b
1115869⟨a, b | aba=ab, abbba=a⟩φ(a) = a, φ(b) = b
1124070⟨a, b | aa=a, aaabbab=a⟩φ(a) = a, φ(b) = b
1124084⟨a, b | aa=a, aababab=a⟩φ(a) = a, φ(b) = b
1124090⟨a, b | aa=a, aabbaab=a⟩φ(a) = a, φ(b) = b
1124110⟨a, b | aa=a, abaabab=a⟩φ(a) = a, φ(b) = b
1124116⟨a, b | aa=a, ababaab=a⟩φ(a) = a, φ(b) = b
1124128⟨a, b | aa=a, abbaaab=a⟩φ(a) = a, φ(b) = b
1124634⟨a, b | aa=a, aabbab=aa⟩φ(a) = a, φ(b) = b
1124657⟨a, b | aa=a, ababab=aa⟩φ(a) = a, φ(b) = b
1124669⟨a, b | aa=a, abbaab=aa⟩φ(a) = a, φ(b) = b
1125198⟨a, b | aa=a, abbab=aaa⟩φ(a) = a, φ(b) = b

Anti-isomorphic instances

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

1 total

Σ#PresentationMapping
1115653⟨a, b | aab=ab, babba=a⟩φ(a) = a, φ(b) = b