#14301 ⟨a, b | abba=b, aabaab=1⟩

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Quick links

  1. Properties
  2. Rewriting system
  3. Isomorphic instances

Properties

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
#RuleProof
1. ab2a ⇒ b [1]
2. ba3 ⇒ a3b [8]
3. (ba)2 ⇒ a2b2 [5]
4. b2a2 ⇒ (ab)2 [10]
5. b3a ⇒ ab3 [3]
6. a(ab)2 ⇒ ba [4]
7. ba2ba ⇒ aba2b [9]
8. a4b2 ⇒ ba2 [7]
9. (a2b)2 ⇒ 1 [2]
10. aba2b2 ⇒ b2a [6]
# 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

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