#12360 ⟨a, b | aaba=ab, abbb=a⟩

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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. a3 ⇒ a [5]
2. aba ⇒ a2b [6]
3. ab2a ⇒ a2b2 [4]
4. ab3 ⇒ a [2]
# ab:aaba=ab,abbb=a ab
aaa=a
aba=aab
abba=aabb
abbb=a

Isomorphic instances

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

3 total

Σ#PresentationMapping
1118712⟨a, b | aaa=a, aabbab=a⟩φ(a) = a, φ(b) = b
1118724⟨a, b | aaa=a, ababab=a⟩φ(a) = a, φ(b) = b
1119273⟨a, b | aaa=a, abbab=aa⟩φ(a) = a, φ(b) = b