#1594 ⟨a, b | aaa=ab, bab=a⟩

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Quick links

  1. Properties
  2. Staircase diagram
  3. Rewriting system
  4. Isomorphic instances

Properties

Staircase diagram

Rewriting system

Format:
Word to reduce:
Tips:
  • Lowercase letters stand for generators.
  • Spaces are ignored.
  • Numbers repeat the previous letter, e.g. b90.
Reduction strategy:
Path to normal form: 1 
1
#RuleProof
1. a5 ⇒ a [5]
2. ba ⇒ a3 [6]
3. ab ⇒ a3 [1]
# ab:aaa=ab,bab=a a/b
aaaaa=a
ba=aaa
ab=aaa

Isomorphic instances

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

26 total

Σ#PresentationMapping
92117⟨a, b | aba=b, abbb=b⟩φ(a) = b, φ(b) = a
92121⟨a, b | aba=b, babb=b⟩φ(a) = b, φ(b) = a
105058⟨a, b | aaa=ab, baaa=a⟩φ(a) = a, φ(b) = b
1112281⟨a, b | aaab=ba, abbb=b⟩φ(a) = b, φ(b) = a
1112361⟨a, b | aaba=ab, abbb=b⟩φ(a) = b, φ(b) = a
1112502⟨a, b | abab=aa, baaa=a⟩φ(a) = a, φ(b) = b
1112593⟨a, b | abba=bb, abbb=b⟩φ(a) = b, φ(b) = a
1112601⟨a, b | abba=bb, babb=b⟩φ(a) = b, φ(b) = a
1119181⟨a, b | aba=b, aababb=b⟩φ(a) = b, φ(b) = a
1119187⟨a, b | aba=b, aabbba=b⟩φ(a) = b, φ(b) = a
1119195⟨a, b | aba=b, abaabb=b⟩φ(a) = b, φ(b) = a
1119197⟨a, b | aba=b, ababab=b⟩φ(a) = b, φ(b) = a
1119199⟨a, b | aba=b, ababba=b⟩φ(a) = b, φ(b) = a
1119217⟨a, b | aba=b, baabab=b⟩φ(a) = b, φ(b) = a
1119731⟨a, b | aba=b, aabbb=ab⟩φ(a) = b, φ(b) = a
1119742⟨a, b | aba=b, ababb=ab⟩φ(a) = b, φ(b) = a
1119743⟨a, b | aba=b, ababb=ba⟩φ(a) = b, φ(b) = a
1119746⟨a, b | aba=b, abbab=ab⟩φ(a) = b, φ(b) = a
1119750⟨a, b | aba=b, abbba=ab⟩φ(a) = b, φ(b) = a
1119761⟨a, b | aba=b, baabb=ba⟩φ(a) = b, φ(b) = a
1119764⟨a, b | aba=b, babab=ab⟩φ(a) = b, φ(b) = a
1120269⟨a, b | aba=b, aaba=bbb⟩φ(a) = b, φ(b) = a
1120293⟨a, b | aba=b, abbb=aab⟩φ(a) = b, φ(b) = a
1120294⟨a, b | aba=b, abbb=aba⟩φ(a) = b, φ(b) = a
1120308⟨a, b | aba=b, babb=aba⟩φ(a) = b, φ(b) = a
1120310⟨a, b | aba=b, babb=baa⟩φ(a) = b, φ(b) = a