#4275 ⟨a, b | aaabb=1, aabba=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. b2 ⇒ c
  2. cb ⇒ bc
  3. ca ⇒ ac
  4. a3b ⇒ ba3
  5. a3c ⇒ 1 
# ab:aaabb=1,aabba=1 bac bb=c frequency:2/0
bb=c
cb=bc
ca=ac
aaab=baaa
aaac=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.

8 total

Σ#PresentationMapping
104280⟨a, b | aaabb=1, abbaa=1⟩φ(a) = a, φ(b) = b
104283⟨a, b | aaabb=1, baaab=1⟩φ(a) = a, φ(b) = b
104289⟨a, b | aaabb=1, bbaaa=1⟩φ(a) = a, φ(b) = b
104322⟨a, b | aabba=1, abbaa=1⟩φ(a) = a, φ(b) = b
104325⟨a, b | aabba=1, baaab=1⟩φ(a) = a, φ(b) = b
1112811⟨a, b | baa=aab, aabbb=1⟩φ(a) = b, φ(b) = a
1112816⟨a, b | baa=aab, abbba=1⟩φ(a) = b, φ(b) = a
1112819⟨a, b | baa=aab, baabb=1⟩φ(a) = b, φ(b) = a