#62 ⟨a, b | ab=a, ba=a⟩

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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. ba ⇒ a 
# ab:ab=a,ba=a ab
ab=a
ba=a

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.

34 total

Σ#PresentationMapping
7269⟨a, b | ab=a, bab=a⟩φ(a) = a, φ(b) = b
7279⟨a, b | ab=a, ba=ab⟩φ(a) = a, φ(b) = b
8942⟨a, b | ab=a, babb=a⟩φ(a) = a, φ(b) = b
81006⟨a, b | ab=a, abb=ba⟩φ(a) = a, φ(b) = b
81013⟨a, b | ab=a, bab=ab⟩φ(a) = a, φ(b) = b
91623⟨a, b | aab=ab, aba=b⟩φ(a) = b, φ(b) = a
92109⟨a, b | aba=b, aaba=b⟩φ(a) = b, φ(b) = a
92982⟨a, b | ab=a, babbb=a⟩φ(a) = a, φ(b) = b
93102⟨a, b | ab=a, abbb=ba⟩φ(a) = a, φ(b) = b
93117⟨a, b | ab=a, babb=ab⟩φ(a) = a, φ(b) = b
93185⟨a, b | ab=a, bab=abb⟩φ(a) = a, φ(b) = b
105131⟨a, b | aab=ab, aaba=b⟩φ(a) = b, φ(b) = a
105251⟨a, b | aba=ab, abaa=b⟩φ(a) = b, φ(b) = a
108806⟨a, b | ab=a, babbbb=a⟩φ(a) = a, φ(b) = b
109046⟨a, b | ab=a, abbbb=ba⟩φ(a) = a, φ(b) = b
109077⟨a, b | ab=a, babbb=ab⟩φ(a) = a, φ(b) = b
109317⟨a, b | ab=a, abbb=bab⟩φ(a) = a, φ(b) = b
109347⟨a, b | ab=a, babb=abb⟩φ(a) = a, φ(b) = b
1112355⟨a, b | aaba=ab, abaa=b⟩φ(a) = b, φ(b) = a
1114606⟨a, b | aaba=b, aaaba=b⟩φ(a) = b, φ(b) = a
1115614⟨a, b | aab=ab, aaaba=b⟩φ(a) = b, φ(b) = a
1115858⟨a, b | aba=ab, abaaa=b⟩φ(a) = b, φ(b) = a
1119169⟨a, b | aba=b, aaabaa=b⟩φ(a) = b, φ(b) = a
1119712⟨a, b | aba=b, aaaba=ab⟩φ(a) = b, φ(b) = a
1119720⟨a, b | aba=b, aabaa=ab⟩φ(a) = b, φ(b) = a
1120255⟨a, b | aba=b, aaab=aab⟩φ(a) = b, φ(b) = a
1120263⟨a, b | aba=b, aaba=aab⟩φ(a) = b, φ(b) = a
1120264⟨a, b | aba=b, aaba=aba⟩φ(a) = b, φ(b) = a
1124522⟨a, b | ab=a, babbbbb=a⟩φ(a) = a, φ(b) = b
1124986⟨a, b | ab=a, abbbbb=ba⟩φ(a) = a, φ(b) = b
1125049⟨a, b | ab=a, babbbb=ab⟩φ(a) = a, φ(b) = b
1125529⟨a, b | ab=a, abbbb=bab⟩φ(a) = a, φ(b) = b
1125591⟨a, b | ab=a, babbb=abb⟩φ(a) = a, φ(b) = b
1125854⟨a, b | ab=a, babb=abbb⟩φ(a) = a, φ(b) = b