#4684 ⟨a, b | aaab=b, abba=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. ba2 ⇒ ab2
  2. b2a ⇒ a2b
  3. a3b ⇒ b
  4. bab2 ⇒ a2ba
  5. b5 ⇒ a(ba)2
  6. (ba)3 ⇒ (ab)3 
# ab:aaab=b,abba=b ab
baa=abb
bba=aab
aaab=b
babb=aaba
bbbbb=ababa
bababa=ababab

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.

2 total

Σ#PresentationMapping
1113077⟨a, b | baa=abb, abba=b⟩φ(a) = a, φ(b) = b
1113078⟨a, b | baa=abb, abbb=a⟩φ(a) = b, φ(b) = a