#3508 ⟨a, b | aa=1, ababa=bb⟩

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Quick links

  1. Properties
  2. Rewriting system
  3. Isomorphic instances

Properties

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. a2 ⇒ 1 [1]
2. ab2 ⇒ (ba)2 [3]
3. (ab)2 ⇒ b2a [4]
# ab:aa=1,ababa=bb a/b
aa=1
abb=baba
abab=bba

Isomorphic instances

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

16 total

Σ#PresentationMapping
93644⟨a, b | aa=1, abab=bba⟩φ(a) = a, φ(b) = b
93650⟨a, b | aa=1, abba=bab⟩φ(a) = a, φ(b) = b
1127009⟨a, b | aa=1, aaababa=bb⟩φ(a) = a, φ(b) = b
1127090⟨a, b | aa=1, abaaaba=bb⟩φ(a) = a, φ(b) = b
1127540⟨a, b | aa=1, aaabab=bba⟩φ(a) = a, φ(b) = b
1127547⟨a, b | aa=1, aaabba=bab⟩φ(a) = a, φ(b) = b
1127569⟨a, b | aa=1, aababa=abb⟩φ(a) = a, φ(b) = b
1127618⟨a, b | aa=1, abaaab=bba⟩φ(a) = a, φ(b) = b
1127624⟨a, b | aa=1, abaaba=bab⟩φ(a) = a, φ(b) = b
1128076⟨a, b | aa=1, aaabb=baba⟩φ(a) = a, φ(b) = b
1128098⟨a, b | aa=1, aabab=abba⟩φ(a) = a, φ(b) = b
1128113⟨a, b | aa=1, aabba=abab⟩φ(a) = a, φ(b) = b
1128150⟨a, b | aa=1, abaab=baba⟩φ(a) = a, φ(b) = b
1128159⟨a, b | aa=1, ababa=aabb⟩φ(a) = a, φ(b) = b
1128163⟨a, b | aa=1, ababa=baab⟩φ(a) = a, φ(b) = b
1128229⟨a, b | aa=1, baaab=abba⟩φ(a) = a, φ(b) = b