#2228 ⟨a, b | ab=aa, aaa=aa⟩

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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. ab ⇒ a2
  2. a3 ⇒ a2 
# ab:ab=aa,aaa=aa ab
ab=aa
aaa=aa

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.

12 total

Σ#PresentationMapping
92229⟨a, b | ab=aa, aaa=ab⟩φ(a) = a, φ(b) = b
92232⟨a, b | ab=aa, aab=aa⟩φ(a) = a, φ(b) = b
92233⟨a, b | ab=aa, aab=ab⟩φ(a) = a, φ(b) = b
92236⟨a, b | ab=aa, aba=aa⟩φ(a) = a, φ(b) = b
92237⟨a, b | ab=aa, aba=ab⟩φ(a) = a, φ(b) = b
92240⟨a, b | ab=aa, abb=aa⟩φ(a) = a, φ(b) = b
92241⟨a, b | ab=aa, abb=ab⟩φ(a) = a, φ(b) = b
1115946⟨a, b | aaa=aa, aaaa=ab⟩φ(a) = a, φ(b) = b
1116094⟨a, b | aab=aa, aabb=ab⟩φ(a) = a, φ(b) = b
1116149⟨a, b | aab=ab, aaab=aa⟩φ(a) = a, φ(b) = b
1116357⟨a, b | aba=aa, abba=ab⟩φ(a) = a, φ(b) = b
1116389⟨a, b | aba=ab, abaa=aa⟩φ(a) = a, φ(b) = b