#1042 ⟨a, b | aa=1, ababab=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. a2 ⇒ 1 [1]
2. b(ab)2 ⇒ a [3]
# ab:aa=1,ababab=1 ab - -
aa=1
babab=a

Isomorphic instances

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

13 total

Σ#PresentationMapping
81128⟨a, b | aa=1, babab=a⟩φ(a) = a, φ(b) = b
105984⟨a, b | aaa=a, ababab=1⟩φ(a) = a, φ(b) = b
106123⟨a, b | aab=b, ababab=1⟩φ(a) = a, φ(b) = b
106144⟨a, b | aab=b, bababa=1⟩φ(a) = a, φ(b) = b
109404⟨a, b | aa=1, aaababab=1⟩φ(a) = a, φ(b) = b
109423⟨a, b | aa=1, aabababa=1⟩φ(a) = a, φ(b) = b
109445⟨a, b | aa=1, abaaabab=1⟩φ(a) = a, φ(b) = b
109454⟨a, b | aa=1, ababaaab=1⟩φ(a) = a, φ(b) = b
109696⟨a, b | aa=1, aababab=a⟩φ(a) = a, φ(b) = b
109730⟨a, b | aa=1, abababa=a⟩φ(a) = a, φ(b) = b
109764⟨a, b | aa=1, baaabab=a⟩φ(a) = a, φ(b) = b
109997⟨a, b | aa=1, ababab=aa⟩φ(a) = a, φ(b) = b
1010318⟨a, b | aa=1, babab=aaa⟩φ(a) = a, φ(b) = b