#14298 ⟨a, b | abba=b, aaabab=1⟩

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Contents

  1. Properties
  2. Rewriting system
  3. Isomorphic instances

Properties

Rewriting system

Format:
Word:
Enter a word above to compute its normal form. Tips:
  • Lowercase letters stand for generators.
  • Spaces are ignored.
  • Numbers repeat the previous letter, e.g. b90.
Strategy:
Result: 1 
1
#RuleProof
1. ba2 ⇒ a2b [5]
2. ab2a ⇒ b [1]
3. (ba)2 ⇒ (ab)2 [7]
4. b3a ⇒ ab3 [3]
5. a3b2 ⇒ ba [4]
6. a3bab ⇒ 1 [2]
7. a2bab2 ⇒ b2a [6]
# ab:abba=b,aaabab=1 ab - -
baa=aab
abba=b
baba=abab
bbba=abbb
aaabb=ba
aaabab=1
aababb=bba

Isomorphic instances

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

2 total

Σ#PresentationMapping
1114302⟨a, b | abba=b, aababa=1⟩φ(a) = a, φ(b) = b
1114308⟨a, b | abba=b, abaaab=1⟩φ(a) = a, φ(b) = b