#2123 ⟨a, b | aba=b, bbbb=b⟩

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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. ba ⇒ ab
  2. a2b ⇒ b
  3. b4 ⇒ b 
# ab:aba=b,bbbb=b ab
ba=ab
aab=b
bbbb=b

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.

17 total

Σ#PresentationMapping
1112605⟨a, b | abba=bb, bbbb=b⟩φ(a) = a, φ(b) = b
1119189⟨a, b | aba=b, aabbbb=b⟩φ(a) = a, φ(b) = b
1119201⟨a, b | aba=b, ababbb=b⟩φ(a) = a, φ(b) = b
1119205⟨a, b | aba=b, abbabb=b⟩φ(a) = a, φ(b) = b
1119207⟨a, b | aba=b, abbbab=b⟩φ(a) = a, φ(b) = b
1119209⟨a, b | aba=b, abbbba=b⟩φ(a) = a, φ(b) = b
1119219⟨a, b | aba=b, baabbb=b⟩φ(a) = a, φ(b) = b
1119221⟨a, b | aba=b, bababb=b⟩φ(a) = a, φ(b) = b
1119223⟨a, b | aba=b, babbab=b⟩φ(a) = a, φ(b) = b
1119227⟨a, b | aba=b, bbaabb=b⟩φ(a) = a, φ(b) = b
1119753⟨a, b | aba=b, abbbb=ab⟩φ(a) = a, φ(b) = b
1119754⟨a, b | aba=b, abbbb=ba⟩φ(a) = a, φ(b) = b
1119767⟨a, b | aba=b, babbb=ab⟩φ(a) = a, φ(b) = b
1119768⟨a, b | aba=b, babbb=ba⟩φ(a) = a, φ(b) = b
1119771⟨a, b | aba=b, bbabb=ab⟩φ(a) = a, φ(b) = b
1120315⟨a, b | aba=b, bbbb=aab⟩φ(a) = a, φ(b) = b
1120316⟨a, b | aba=b, bbbb=aba⟩φ(a) = a, φ(b) = b