#40 ⟨a, b | aa=a, bbb=1⟩

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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 ⇒ a [1]
2. b3 ⇒ 1 [2]
# ab:aa=a,bbb=1 ab
aa=a
bbb=1

Isomorphic instances

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

11 total

Σ#PresentationMapping
8419⟨a, b | aab=ab, bbb=1⟩φ(a) = a, φ(b) = b
92423⟨a, b | aaa=1, aaabb=b⟩φ(a) = b, φ(b) = a
92445⟨a, b | aaa=1, baaab=b⟩φ(a) = b, φ(b) = a
92566⟨a, b | aaa=1, aaab=bb⟩φ(a) = b, φ(b) = a
108047⟨a, b | aaa=1, aabb=aab⟩φ(a) = b, φ(b) = a
108064⟨a, b | aaa=1, abba=aba⟩φ(a) = b, φ(b) = a
1122204⟨a, b | aaa=1, aaaabb=ab⟩φ(a) = b, φ(b) = a
1122217⟨a, b | aaa=1, aaabba=ba⟩φ(a) = b, φ(b) = a
1122251⟨a, b | aaa=1, abaaab=ab⟩φ(a) = b, φ(b) = a
1122729⟨a, b | aaa=1, aaaab=abb⟩φ(a) = b, φ(b) = a
1122740⟨a, b | aaa=1, aaaba=bba⟩φ(a) = b, φ(b) = a