#73 ⟨a, b | aa=1, bbbb=1⟩

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Properties

Complete 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
  1. a2 ⇒ 1
  2. b4 ⇒ 1 
# ab:aa=1,bbbb=1 ab
aa=1
bbbb=1

Right Cayley graph (truncated)

Left Cayley graph (truncated)

Other isomorphic instances

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

46 total

Σ#PresentationMapping
8542⟨a, b | aab=b, bbbb=1⟩φ(a) = a, φ(b) = b
81038⟨a, b | aa=1, aabbbb=1⟩φ(a) = a, φ(b) = b
81048⟨a, b | aa=1, abbbba=1⟩φ(a) = a, φ(b) = b
81053⟨a, b | aa=1, baabbb=1⟩φ(a) = a, φ(b) = b
81057⟨a, b | aa=1, bbaabb=1⟩φ(a) = a, φ(b) = b
81122⟨a, b | aa=1, abbbb=a⟩φ(a) = a, φ(b) = b
81201⟨a, b | aa=1, bbbb=aa⟩φ(a) = a, φ(b) = b
103917⟨a, b | aabb=bb, bbbb=1⟩φ(a) = a, φ(b) = b
103988⟨a, b | baab=bb, bbbb=1⟩φ(a) = a, φ(b) = b
105425⟨a, b | aaaa=1, aaaabb=1⟩φ(a) = b, φ(b) = a
105428⟨a, b | aaaa=1, aaabba=1⟩φ(a) = b, φ(b) = a
105433⟨a, b | aaaa=1, aabbaa=1⟩φ(a) = b, φ(b) = a
105448⟨a, b | aaaa=1, baaaab=1⟩φ(a) = b, φ(b) = a
105980⟨a, b | aaa=a, aabbbb=1⟩φ(a) = a, φ(b) = b
105990⟨a, b | aaa=a, abbbba=1⟩φ(a) = a, φ(b) = b
105995⟨a, b | aaa=a, baabbb=1⟩φ(a) = a, φ(b) = b
105999⟨a, b | aaa=a, bbaabb=1⟩φ(a) = a, φ(b) = b
106117⟨a, b | aab=b, aabbbb=1⟩φ(a) = a, φ(b) = b
106132⟨a, b | aab=b, abbbba=1⟩φ(a) = a, φ(b) = b
106141⟨a, b | aab=b, baabbb=1⟩φ(a) = a, φ(b) = b
106153⟨a, b | aab=b, bbaabb=1⟩φ(a) = a, φ(b) = b
106159⟨a, b | aab=b, bbbaab=1⟩φ(a) = a, φ(b) = b
106162⟨a, b | aab=b, bbbbaa=1⟩φ(a) = a, φ(b) = b
109399⟨a, b | aa=1, aaaabbbb=1⟩φ(a) = a, φ(b) = b
109413⟨a, b | aa=1, aaabbbba=1⟩φ(a) = a, φ(b) = b
109421⟨a, b | aa=1, aabaabbb=1⟩φ(a) = a, φ(b) = b
109431⟨a, b | aa=1, aabbaabb=1⟩φ(a) = a, φ(b) = b
109435⟨a, b | aa=1, aabbbaab=1⟩φ(a) = a, φ(b) = b
109438⟨a, b | aa=1, aabbbbaa=1⟩φ(a) = a, φ(b) = b
109452⟨a, b | aa=1, abaabbba=1⟩φ(a) = a, φ(b) = b
109468⟨a, b | aa=1, abbaabba=1⟩φ(a) = a, φ(b) = b
109487⟨a, b | aa=1, baaaabbb=1⟩φ(a) = a, φ(b) = b
109492⟨a, b | aa=1, baabaabb=1⟩φ(a) = a, φ(b) = b
109495⟨a, b | aa=1, baabbaab=1⟩φ(a) = a, φ(b) = b
109510⟨a, b | aa=1, bbaaaabb=1⟩φ(a) = a, φ(b) = b
109686⟨a, b | aa=1, aaabbbb=a⟩φ(a) = a, φ(b) = b
109712⟨a, b | aa=1, aabbbba=a⟩φ(a) = a, φ(b) = b
109726⟨a, b | aa=1, abaabbb=a⟩φ(a) = a, φ(b) = b
109742⟨a, b | aa=1, abbaabb=a⟩φ(a) = a, φ(b) = b
109750⟨a, b | aa=1, abbbaab=a⟩φ(a) = a, φ(b) = b
109982⟨a, b | aa=1, aabbbb=aa⟩φ(a) = a, φ(b) = b
1010021⟨a, b | aa=1, abbbba=aa⟩φ(a) = a, φ(b) = b
1010039⟨a, b | aa=1, baabbb=aa⟩φ(a) = a, φ(b) = b
1010054⟨a, b | aa=1, bbaabb=aa⟩φ(a) = a, φ(b) = b
1010296⟨a, b | aa=1, abbbb=aaa⟩φ(a) = a, φ(b) = b
1010529⟨a, b | aa=1, bbbb=aaaa⟩φ(a) = a, φ(b) = b