#7788 ⟨a, b | aaa=1, ababa=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. a3 ⇒ 1
  2. (ba)2 ⇒ a2b2
  3. b2a2 ⇒ (ab)2
  4. b3a ⇒ ab3 
# ab:aaa=1,ababa=bb ab
aaa=1
baba=aabb
bbaa=abab
bbba=abbb

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.

1 total

Σ#PresentationMapping
1123301⟨a, b | aaa=1, baba=aabb⟩φ(a) = a, φ(b) = b

Other anti-isomorphic instances

The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.

1 total

Σ#PresentationMapping
1123299⟨a, b | aaa=1, baab=abba⟩φ(a) = aa, φ(b) = b