#240 ⟨a, b | aa=a, aba=b⟩

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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. ab ⇒ b
  3. ba ⇒ b 
# ab:aa=a,aba=b ab
aa=a
ab=b
ba=b

Staircase diagram

Right 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
8885⟨a, b | aa=a, aaba=b⟩φ(a) = a, φ(b) = b
92861⟨a, b | aa=a, aaaba=b⟩φ(a) = a, φ(b) = b
92865⟨a, b | aa=a, aabaa=b⟩φ(a) = a, φ(b) = b
108573⟨a, b | aa=a, aaaaba=b⟩φ(a) = a, φ(b) = b
108577⟨a, b | aa=a, aaabaa=b⟩φ(a) = a, φ(b) = b
1124049⟨a, b | aa=a, aaaaaba=b⟩φ(a) = a, φ(b) = b
1124053⟨a, b | aa=a, aaaabaa=b⟩φ(a) = a, φ(b) = b
1124061⟨a, b | aa=a, aaabaaa=b⟩φ(a) = a, φ(b) = b