#992 ⟨a, b | ab=a, 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 ⇒ a
  2. a3 ⇒ a2 
# ab:ab=a,aaa=aa ab
ab=a
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.

55 total

Σ#PresentationMapping
93076⟨a, b | ab=a, aaab=aa⟩φ(a) = a, φ(b) = b
93080⟨a, b | ab=a, aaba=aa⟩φ(a) = a, φ(b) = b
93088⟨a, b | ab=a, abaa=aa⟩φ(a) = a, φ(b) = b
93172⟨a, b | ab=a, aab=aaa⟩φ(a) = a, φ(b) = b
93173⟨a, b | ab=a, aba=aaa⟩φ(a) = a, φ(b) = b
108996⟨a, b | ab=a, aaabb=aa⟩φ(a) = a, φ(b) = b
109004⟨a, b | ab=a, aabab=aa⟩φ(a) = a, φ(b) = b
109008⟨a, b | ab=a, aabba=aa⟩φ(a) = a, φ(b) = b
109020⟨a, b | ab=a, abaab=aa⟩φ(a) = a, φ(b) = b
109024⟨a, b | ab=a, ababa=aa⟩φ(a) = a, φ(b) = b
109032⟨a, b | ab=a, abbaa=aa⟩φ(a) = a, φ(b) = b
109265⟨a, b | ab=a, aaab=aab⟩φ(a) = a, φ(b) = b
109266⟨a, b | ab=a, aaab=aba⟩φ(a) = a, φ(b) = b
109273⟨a, b | ab=a, aaba=aab⟩φ(a) = a, φ(b) = b
109274⟨a, b | ab=a, aaba=aba⟩φ(a) = a, φ(b) = b
109280⟨a, b | ab=a, aabb=aaa⟩φ(a) = a, φ(b) = b
109289⟨a, b | ab=a, abaa=aab⟩φ(a) = a, φ(b) = b
109290⟨a, b | ab=a, abaa=aba⟩φ(a) = a, φ(b) = b
109296⟨a, b | ab=a, abab=aaa⟩φ(a) = a, φ(b) = b
109304⟨a, b | ab=a, abba=aaa⟩φ(a) = a, φ(b) = b
1124888⟨a, b | ab=a, aaabbb=aa⟩φ(a) = a, φ(b) = b
1124904⟨a, b | ab=a, aababb=aa⟩φ(a) = a, φ(b) = b
1124912⟨a, b | ab=a, aabbab=aa⟩φ(a) = a, φ(b) = b
1124916⟨a, b | ab=a, aabbba=aa⟩φ(a) = a, φ(b) = b
1124936⟨a, b | ab=a, abaabb=aa⟩φ(a) = a, φ(b) = b
1124944⟨a, b | ab=a, ababab=aa⟩φ(a) = a, φ(b) = b
1124948⟨a, b | ab=a, ababba=aa⟩φ(a) = a, φ(b) = b
1124960⟨a, b | ab=a, abbaab=aa⟩φ(a) = a, φ(b) = b
1124964⟨a, b | ab=a, abbaba=aa⟩φ(a) = a, φ(b) = b
1124972⟨a, b | ab=a, abbbaa=aa⟩φ(a) = a, φ(b) = b
1125429⟨a, b | ab=a, aaabb=aab⟩φ(a) = a, φ(b) = b
1125430⟨a, b | ab=a, aaabb=aba⟩φ(a) = a, φ(b) = b
1125445⟨a, b | ab=a, aabab=aab⟩φ(a) = a, φ(b) = b
1125446⟨a, b | ab=a, aabab=aba⟩φ(a) = a, φ(b) = b
1125453⟨a, b | ab=a, aabba=aab⟩φ(a) = a, φ(b) = b
1125454⟨a, b | ab=a, aabba=aba⟩φ(a) = a, φ(b) = b
1125460⟨a, b | ab=a, aabbb=aaa⟩φ(a) = a, φ(b) = b
1125477⟨a, b | ab=a, abaab=aab⟩φ(a) = a, φ(b) = b
1125478⟨a, b | ab=a, abaab=aba⟩φ(a) = a, φ(b) = b
1125485⟨a, b | ab=a, ababa=aab⟩φ(a) = a, φ(b) = b
1125486⟨a, b | ab=a, ababa=aba⟩φ(a) = a, φ(b) = b
1125492⟨a, b | ab=a, ababb=aaa⟩φ(a) = a, φ(b) = b
1125501⟨a, b | ab=a, abbaa=aab⟩φ(a) = a, φ(b) = b
1125502⟨a, b | ab=a, abbaa=aba⟩φ(a) = a, φ(b) = b
1125508⟨a, b | ab=a, abbab=aaa⟩φ(a) = a, φ(b) = b
1125516⟨a, b | ab=a, abbba=aaa⟩φ(a) = a, φ(b) = b
1125796⟨a, b | ab=a, aabb=aaab⟩φ(a) = a, φ(b) = b
1125797⟨a, b | ab=a, aabb=aaba⟩φ(a) = a, φ(b) = b
1125801⟨a, b | ab=a, abaa=aabb⟩φ(a) = a, φ(b) = b
1125803⟨a, b | ab=a, abab=aaab⟩φ(a) = a, φ(b) = b
1125804⟨a, b | ab=a, abab=aaba⟩φ(a) = a, φ(b) = b
1125806⟨a, b | ab=a, abab=abaa⟩φ(a) = a, φ(b) = b
1125808⟨a, b | ab=a, abba=aaab⟩φ(a) = a, φ(b) = b
1125809⟨a, b | ab=a, abba=aaba⟩φ(a) = a, φ(b) = b
1125811⟨a, b | ab=a, abba=abaa⟩φ(a) = a, φ(b) = b