#19733 ⟨a, b | aba=b, aabbb=bb⟩

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  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. aba ⇒ b [1]
2. b2a ⇒ ab2 [3]
3. b3 ⇒ b2 [8]
4. a2b2 ⇒ b2 [9]
5. bab2 ⇒ ab2 [5]
# ab:aba=b,aabbb=bb ab
aba=b
bba=abb
bbb=bb
aabb=bb
babb=abb

Isomorphic instances

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

6 total

Σ#PresentationMapping
1119744⟨a, b | aba=b, ababb=bb⟩φ(a) = a, φ(b) = b
1119748⟨a, b | aba=b, abbab=bb⟩φ(a) = a, φ(b) = b
1119751⟨a, b | aba=b, abbba=bb⟩φ(a) = a, φ(b) = b
1119762⟨a, b | aba=b, baabb=bb⟩φ(a) = a, φ(b) = b
1119765⟨a, b | aba=b, babab=bb⟩φ(a) = a, φ(b) = b
1120285⟨a, b | aba=b, abab=bbb⟩φ(a) = a, φ(b) = b