#767 ⟨a, b | aab=1, abab=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. a2b ⇒ 1
  2. bab ⇒ ab2 
# ab:aab=1,abab=b ab
aab=1
bab=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.

13 total

Σ#PresentationMapping
107866⟨a, b | aab=1, ababa=ba⟩φ(a) = a, φ(b) = b
107879⟨a, b | aab=1, abbab=bb⟩φ(a) = a, φ(b) = b
107911⟨a, b | aab=1, babab=bb⟩φ(a) = a, φ(b) = b
1121819⟨a, b | aab=1, aaabbab=b⟩φ(a) = a, φ(b) = b
1121835⟨a, b | aab=1, aababab=b⟩φ(a) = a, φ(b) = b
1121863⟨a, b | aab=1, abaaabb=b⟩φ(a) = a, φ(b) = b
1121867⟨a, b | aab=1, abaabab=b⟩φ(a) = a, φ(b) = b
1121875⟨a, b | aab=1, ababaab=b⟩φ(a) = a, φ(b) = b
1123343⟨a, b | aab=1, abab=aabb⟩φ(a) = a, φ(b) = b
1123371⟨a, b | aab=1, baab=abab⟩φ(a) = a, φ(b) = b
1123381⟨a, b | aab=1, baba=abba⟩φ(a) = a, φ(b) = b
1123415⟨a, b | aab=1, bbab=abbb⟩φ(a) = a, φ(b) = b
1123419⟨a, b | aab=1, bbab=babb⟩φ(a) = a, φ(b) = b