#3770 ⟨a, b | aaaa=bb, aabb=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. a6 ⇒ 1
  2. a2b ⇒ ba2
  3. b2 ⇒ a4 
# ab:aaaa=bb,aabb=1 a/b
aaaaaa=1
aab=baa
bb=aaaa

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.

5 total

Σ#PresentationMapping
103772⟨a, b | aaaa=bb, abba=1⟩φ(a) = a, φ(b) = b
103774⟨a, b | aaaa=bb, baab=1⟩φ(a) = a, φ(b) = b
105586⟨a, b | aabb=1, aaaaaa=1⟩φ(a) = a, φ(b) = b
105658⟨a, b | abba=1, aaaaaa=1⟩φ(a) = a, φ(b) = b
105693⟨a, b | abba=1, bbbbbb=1⟩φ(a) = a, φ(b) = b