#994 ⟨a, b | ab=a, aaa=ba⟩

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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. a4 ⇒ a2
  2. ba ⇒ a3
  3. ab ⇒ a 
# ab:ab=a,aaa=ba a/b
aaaa=aa
ba=aaa
ab=a

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.

34 total

Σ#PresentationMapping
93078⟨a, b | ab=a, aaab=ba⟩φ(a) = a, φ(b) = b
93082⟨a, b | ab=a, aaba=ba⟩φ(a) = a, φ(b) = b
93090⟨a, b | ab=a, abaa=ba⟩φ(a) = a, φ(b) = b
93182⟨a, b | ab=a, bab=aaa⟩φ(a) = a, φ(b) = b
108998⟨a, b | ab=a, aaabb=ba⟩φ(a) = a, φ(b) = b
109006⟨a, b | ab=a, aabab=ba⟩φ(a) = a, φ(b) = b
109010⟨a, b | ab=a, aabba=ba⟩φ(a) = a, φ(b) = b
109022⟨a, b | ab=a, abaab=ba⟩φ(a) = a, φ(b) = b
109026⟨a, b | ab=a, ababa=ba⟩φ(a) = a, φ(b) = b
109034⟨a, b | ab=a, abbaa=ba⟩φ(a) = a, φ(b) = b
109269⟨a, b | ab=a, aaab=bab⟩φ(a) = a, φ(b) = b
109277⟨a, b | ab=a, aaba=bab⟩φ(a) = a, φ(b) = b
109293⟨a, b | ab=a, abaa=bab⟩φ(a) = a, φ(b) = b
109344⟨a, b | ab=a, babb=aaa⟩φ(a) = a, φ(b) = b
1124890⟨a, b | ab=a, aaabbb=ba⟩φ(a) = a, φ(b) = b
1124906⟨a, b | ab=a, aababb=ba⟩φ(a) = a, φ(b) = b
1124914⟨a, b | ab=a, aabbab=ba⟩φ(a) = a, φ(b) = b
1124918⟨a, b | ab=a, aabbba=ba⟩φ(a) = a, φ(b) = b
1124938⟨a, b | ab=a, abaabb=ba⟩φ(a) = a, φ(b) = b
1124946⟨a, b | ab=a, ababab=ba⟩φ(a) = a, φ(b) = b
1124950⟨a, b | ab=a, ababba=ba⟩φ(a) = a, φ(b) = b
1124962⟨a, b | ab=a, abbaab=ba⟩φ(a) = a, φ(b) = b
1124966⟨a, b | ab=a, abbaba=ba⟩φ(a) = a, φ(b) = b
1124974⟨a, b | ab=a, abbbaa=ba⟩φ(a) = a, φ(b) = b
1125433⟨a, b | ab=a, aaabb=bab⟩φ(a) = a, φ(b) = b
1125449⟨a, b | ab=a, aabab=bab⟩φ(a) = a, φ(b) = b
1125457⟨a, b | ab=a, aabba=bab⟩φ(a) = a, φ(b) = b
1125481⟨a, b | ab=a, abaab=bab⟩φ(a) = a, φ(b) = b
1125489⟨a, b | ab=a, ababa=bab⟩φ(a) = a, φ(b) = b
1125505⟨a, b | ab=a, abbaa=bab⟩φ(a) = a, φ(b) = b
1125588⟨a, b | ab=a, babbb=aaa⟩φ(a) = a, φ(b) = b
1125848⟨a, b | ab=a, babb=aaab⟩φ(a) = a, φ(b) = b
1125849⟨a, b | ab=a, babb=aaba⟩φ(a) = a, φ(b) = b
1125851⟨a, b | ab=a, babb=abaa⟩φ(a) = a, φ(b) = b