#14301 ⟨a, b | abba=b, aabaab=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. ab2a ⇒ b
  2. ba3 ⇒ a3b
  3. (ba)2 ⇒ a2b2
  4. b2a2 ⇒ (ab)2
  5. b3a ⇒ ab3
  6. a(ab)2 ⇒ ba
  7. ba2ba ⇒ aba2b
  8. a4b2 ⇒ ba2
  9. (a2b)2 ⇒ 1
  10. aba2b2 ⇒ b2a 
# ab:abba=b,aabaab=1 ab
abba=b
baaa=aaab
baba=aabb
bbaa=abab
bbba=abbb
aabab=ba
baaba=abaab
aaaabb=baa
aabaab=1
abaabb=bba

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
1114309⟨a, b | abba=b, abaaba=1⟩φ(a) = a, φ(b) = b