#1590 ⟨a, b | aaa=ab, abb=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. a5 ⇒ a [2]
2. ab ⇒ a3 [1]
# ab:aaa=ab,abb=a a/b - -
aaaaa=a
ab=aaa

Isomorphic instances

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

5 total

Σ#PresentationMapping
105044⟨a, b | aaa=ab, aaab=a⟩φ(a) = a, φ(b) = b
105046⟨a, b | aaa=ab, aaba=a⟩φ(a) = a, φ(b) = b
105050⟨a, b | aaa=ab, abaa=a⟩φ(a) = a, φ(b) = b
1114409⟨a, b | aaab=a, aaaaa=a⟩φ(a) = a, φ(b) = b
1115441⟨a, b | aaa=ab, aaaaa=a⟩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.

18 total

Σ#PresentationMapping
92067⟨a, b | aab=b, abbb=b⟩φ(a) = b, φ(b) = a
1112253⟨a, b | aaab=ab, abbb=b⟩φ(a) = b, φ(b) = a
1112387⟨a, b | aaba=ba, abbb=b⟩φ(a) = b, φ(b) = a
1112485⟨a, b | aabb=bb, abbb=b⟩φ(a) = b, φ(b) = a
1112547⟨a, b | abab=bb, abbb=b⟩φ(a) = b, φ(b) = a
1112549⟨a, b | abab=bb, babb=b⟩φ(a) = b, φ(b) = a
1112551⟨a, b | abab=bb, bbab=b⟩φ(a) = b, φ(b) = a
1112556⟨a, b | abba=aa, baaa=a⟩φ(a) = a, φ(b) = b
1118975⟨a, b | aab=b, aaabbb=b⟩φ(a) = b, φ(b) = a
1118999⟨a, b | aab=b, abaabb=b⟩φ(a) = b, φ(b) = a
1119003⟨a, b | aab=b, ababab=b⟩φ(a) = b, φ(b) = a
1119011⟨a, b | aab=b, abbaab=b⟩φ(a) = b, φ(b) = a
1119533⟨a, b | aab=b, aabbb=ab⟩φ(a) = b, φ(b) = a
1119581⟨a, b | aab=b, baabb=ab⟩φ(a) = b, φ(b) = a
1119589⟨a, b | aab=b, babab=ab⟩φ(a) = b, φ(b) = a
1119605⟨a, b | aab=b, bbaab=ab⟩φ(a) = b, φ(b) = a
1120063⟨a, b | aab=b, aaab=bbb⟩φ(a) = b, φ(b) = a
1120105⟨a, b | aab=b, abbb=aab⟩φ(a) = b, φ(b) = a