#3940 ⟨a, b | abab=ba, abba=1⟩

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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. ba2 ⇒ a2b
  2. b2a ⇒ ab2
  3. a2b2 ⇒ 1
  4. (ab)2 ⇒ ba
  5. (ba)2 ⇒ ab 
# ab:abab=ba,abba=1 ab
baa=aab
bba=abb
aabb=1
abab=ba
baba=ab

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.

4 total

Σ#PresentationMapping
103945⟨a, b | abab=ba, bbaa=1⟩φ(a) = a, φ(b) = b
103990⟨a, b | baba=ab, bbaa=1⟩φ(a) = a, φ(b) = b
105617⟨a, b | aabb=1, bababa=1⟩φ(a) = a, φ(b) = b
105676⟨a, b | abba=1, ababab=1⟩φ(a) = a, φ(b) = b