#960 ⟨a, b | aa=a, aba=ab⟩

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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. ab ⇒ c
  4. ca ⇒ c
  5. cb ⇒ c2 
# ab:aa=a,aba=ab acb ab=c frequency:2/1
aa=a
ac=c
ab=c
ca=c
cb=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.

13 total

Σ#PresentationMapping
93008⟨a, b | aa=a, aaba=ab⟩φ(a) = a, φ(b) = b
93138⟨a, b | aa=a, aba=aab⟩φ(a) = a, φ(b) = b
108848⟨a, b | aa=a, aaaba=ab⟩φ(a) = a, φ(b) = b
108856⟨a, b | aa=a, aabaa=ab⟩φ(a) = a, φ(b) = b
109120⟨a, b | aa=a, aaab=aba⟩φ(a) = a, φ(b) = b
109127⟨a, b | aa=a, aaba=aab⟩φ(a) = a, φ(b) = b
1124596⟨a, b | aa=a, aaaaba=ab⟩φ(a) = a, φ(b) = b
1124604⟨a, b | aa=a, aaabaa=ab⟩φ(a) = a, φ(b) = b
1125124⟨a, b | aa=a, aaaab=aba⟩φ(a) = a, φ(b) = b
1125131⟨a, b | aa=a, aaaba=aab⟩φ(a) = a, φ(b) = b
1125147⟨a, b | aa=a, aabaa=aab⟩φ(a) = a, φ(b) = b
1125662⟨a, b | aa=a, aaba=aaab⟩φ(a) = a, φ(b) = b
1125666⟨a, b | aa=a, abaa=aaab⟩φ(a) = a, φ(b) = b