#20920 ⟨a, b | ab=aa, aaaa=aaa⟩

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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. a4 ⇒ a3 
# ab:ab=aa,aaaa=aaa ab
ab=aa
aaaa=aaa

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.

31 total

Σ#PresentationMapping
1120921⟨a, b | ab=aa, aaaa=aab⟩φ(a) = a, φ(b) = b
1120922⟨a, b | ab=aa, aaaa=aba⟩φ(a) = a, φ(b) = b
1120923⟨a, b | ab=aa, aaaa=abb⟩φ(a) = a, φ(b) = b
1120928⟨a, b | ab=aa, aaab=aaa⟩φ(a) = a, φ(b) = b
1120929⟨a, b | ab=aa, aaab=aab⟩φ(a) = a, φ(b) = b
1120930⟨a, b | ab=aa, aaab=aba⟩φ(a) = a, φ(b) = b
1120931⟨a, b | ab=aa, aaab=abb⟩φ(a) = a, φ(b) = b
1120936⟨a, b | ab=aa, aaba=aaa⟩φ(a) = a, φ(b) = b
1120937⟨a, b | ab=aa, aaba=aab⟩φ(a) = a, φ(b) = b
1120938⟨a, b | ab=aa, aaba=aba⟩φ(a) = a, φ(b) = b
1120939⟨a, b | ab=aa, aaba=abb⟩φ(a) = a, φ(b) = b
1120944⟨a, b | ab=aa, aabb=aaa⟩φ(a) = a, φ(b) = b
1120945⟨a, b | ab=aa, aabb=aab⟩φ(a) = a, φ(b) = b
1120946⟨a, b | ab=aa, aabb=aba⟩φ(a) = a, φ(b) = b
1120947⟨a, b | ab=aa, aabb=abb⟩φ(a) = a, φ(b) = b
1120952⟨a, b | ab=aa, abaa=aaa⟩φ(a) = a, φ(b) = b
1120953⟨a, b | ab=aa, abaa=aab⟩φ(a) = a, φ(b) = b
1120954⟨a, b | ab=aa, abaa=aba⟩φ(a) = a, φ(b) = b
1120955⟨a, b | ab=aa, abaa=abb⟩φ(a) = a, φ(b) = b
1120960⟨a, b | ab=aa, abab=aaa⟩φ(a) = a, φ(b) = b
1120961⟨a, b | ab=aa, abab=aab⟩φ(a) = a, φ(b) = b
1120962⟨a, b | ab=aa, abab=aba⟩φ(a) = a, φ(b) = b
1120963⟨a, b | ab=aa, abab=abb⟩φ(a) = a, φ(b) = b
1120968⟨a, b | ab=aa, abba=aaa⟩φ(a) = a, φ(b) = b
1120969⟨a, b | ab=aa, abba=aab⟩φ(a) = a, φ(b) = b
1120970⟨a, b | ab=aa, abba=aba⟩φ(a) = a, φ(b) = b
1120971⟨a, b | ab=aa, abba=abb⟩φ(a) = a, φ(b) = b
1120976⟨a, b | ab=aa, abbb=aaa⟩φ(a) = a, φ(b) = b
1120977⟨a, b | ab=aa, abbb=aab⟩φ(a) = a, φ(b) = b
1120978⟨a, b | ab=aa, abbb=aba⟩φ(a) = a, φ(b) = b
1120979⟨a, b | ab=aa, abbb=abb⟩φ(a) = a, φ(b) = b