#3009 ⟨a, b | aa=a, aaba=ba⟩

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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 ⇒ a
  2. ac ⇒ c
  3. ca ⇒ c
  4. ba ⇒ c
  5. bc ⇒ c2 
# ab:aa=a,aaba=ba acb ba=c frequency:2/1
aa=a
ac=c
ca=c
ba=c
bc=cc

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
108849⟨a, b | aa=a, aaaba=ba⟩φ(a) = a, φ(b) = b
109130⟨a, b | aa=a, aaba=baa⟩φ(a) = a, φ(b) = b
1124597⟨a, b | aa=a, aaaaba=ba⟩φ(a) = a, φ(b) = b
1124605⟨a, b | aa=a, aaabaa=ba⟩φ(a) = a, φ(b) = b
1125134⟨a, b | aa=a, aaaba=baa⟩φ(a) = a, φ(b) = b