#2270 ⟨a, b | bb=aa, aaa=aa⟩

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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 ⇒ b2 [1]
2. b2a ⇒ b2 [2]
3. ab2 ⇒ b2 [3]
4. b4 ⇒ b2 [4]
# ab:bb=aa,aaa=aa ba
aa=bb
bba=bb
abb=bb
bbbb=bb

Isomorphic instances

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

6 total

Σ#PresentationMapping
92272⟨a, b | bb=aa, aaa=bb⟩φ(a) = a, φ(b) = b
92273⟨a, b | bb=aa, aab=aa⟩φ(a) = b, φ(b) = a
92276⟨a, b | bb=aa, aab=bb⟩φ(a) = b, φ(b) = a
1115947⟨a, b | aaa=aa, aaaa=bb⟩φ(a) = a, φ(b) = b
1116096⟨a, b | aab=aa, aabb=bb⟩φ(a) = b, φ(b) = a
1116108⟨a, b | aab=aa, abba=bb⟩φ(a) = b, φ(b) = a