#7788 ⟨a, b | aaa=1, ababa=bb⟩

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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. a3 ⇒ 1 [1]
2. (ba)2 ⇒ a2b2 [3]
3. b2a2 ⇒ (ab)2 [4]
4. b3a ⇒ ab3 [5]
# ab:aaa=1,ababa=bb ab
aaa=1
baba=aabb
bbaa=abab
bbba=abbb

Isomorphic instances

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

2 total

Σ#PresentationMapping
1123299⟨a, b | aaa=1, baab=abba⟩φ(a) = a, φ(b) = aabaa
1123301⟨a, b | aaa=1, baba=aabb⟩φ(a) = a, φ(b) = b