#2984 ⟨a, b | ab=a, bbaaa=a⟩

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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. ab ⇒ a [1]
2. a3 ⇒ a [5]
3. b2a ⇒ a [6]
# ab:ab=a,bbaaa=a ab
ab=a
aaa=a
bba=a

Isomorphic instances

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

16 total

Σ#PresentationMapping
108810⟨a, b | ab=a, bbaaab=a⟩φ(a) = a, φ(b) = b
108812⟨a, b | ab=a, bbaaba=a⟩φ(a) = a, φ(b) = b
108816⟨a, b | ab=a, bbabaa=a⟩φ(a) = a, φ(b) = b
109081⟨a, b | ab=a, bbaaa=ab⟩φ(a) = a, φ(b) = b
1114457⟨a, b | aaab=a, bbaaa=a⟩φ(a) = a, φ(b) = b
1115593⟨a, b | aab=aa, bbaaa=a⟩φ(a) = a, φ(b) = b
1124530⟨a, b | ab=a, bbaaabb=a⟩φ(a) = a, φ(b) = b
1124534⟨a, b | ab=a, bbaabab=a⟩φ(a) = a, φ(b) = b
1124536⟨a, b | ab=a, bbaabba=a⟩φ(a) = a, φ(b) = b
1124542⟨a, b | ab=a, bbabaab=a⟩φ(a) = a, φ(b) = b
1124544⟨a, b | ab=a, bbababa=a⟩φ(a) = a, φ(b) = b
1124548⟨a, b | ab=a, bbabbaa=a⟩φ(a) = a, φ(b) = b
1125057⟨a, b | ab=a, bbaaab=ab⟩φ(a) = a, φ(b) = b
1125061⟨a, b | ab=a, bbaaba=ab⟩φ(a) = a, φ(b) = b
1125069⟨a, b | ab=a, bbabaa=ab⟩φ(a) = a, φ(b) = b
1125599⟨a, b | ab=a, bbaaa=abb⟩φ(a) = a, φ(b) = b