#456 ⟨a, b | aaaa=1, abab=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. bab ⇒ a3
  2. a4 ⇒ 1 
# ab:aaaa=1,abab=1 ab
bab=aaa
aaaa=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.

7 total

Σ#PresentationMapping
104098⟨a, b | bab=aaa, aaaa=1⟩φ(a) = a, φ(b) = b
104102⟨a, b | bab=aaa, abab=1⟩φ(a) = a, φ(b) = b
105704⟨a, b | aaaa=1, aabab=a⟩φ(a) = a, φ(b) = b
105712⟨a, b | aaaa=1, ababa=a⟩φ(a) = a, φ(b) = b
105894⟨a, b | abab=1, aaaaa=a⟩φ(a) = a, φ(b) = b
105897⟨a, b | abab=1, aaaab=b⟩φ(a) = a, φ(b) = b
105919⟨a, b | abab=1, baaaa=b⟩φ(a) = a, φ(b) = b