#1189 ⟨a, b | aa=1, abba=bb⟩

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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. a2 ⇒ 1
  2. b2a ⇒ ab2 
# ab:aa=1,abba=bb ab
aa=1
bba=abb

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.

10 total

Σ#PresentationMapping
81252⟨a, b | aa=1, bba=abb⟩φ(a) = a, φ(b) = b
109954⟨a, b | aa=1, aaabba=bb⟩φ(a) = a, φ(b) = b
109992⟨a, b | aa=1, abaaba=bb⟩φ(a) = a, φ(b) = b
1010228⟨a, b | aa=1, aaabb=bba⟩φ(a) = a, φ(b) = b
1010247⟨a, b | aa=1, aabba=abb⟩φ(a) = a, φ(b) = b
1010266⟨a, b | aa=1, abaab=bba⟩φ(a) = a, φ(b) = b
1010272⟨a, b | aa=1, ababa=bab⟩φ(a) = a, φ(b) = ba
1010489⟨a, b | aa=1, abba=aabb⟩φ(a) = a, φ(b) = b
1010507⟨a, b | aa=1, baab=abba⟩φ(a) = a, φ(b) = b
1010510⟨a, b | aa=1, baba=abab⟩φ(a) = a, φ(b) = ba