#2184 ⟨a, b, c | aabb=1, bcbc=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. (bc)2 ⇒ 1 [2]
2. (cb)2 ⇒ 1 [4]
3. b2a ⇒ ab2 [10]
4. cbca ⇒ ba(cbc)2 [7]
5. a2 ⇒ (cbc)2 [5]
# abc:aabb=1,bcbc=1 bc/a - -
bcbc=1
cbcb=1
bba=abb
cbca=bacbccbc
aa=cbccbc

Isomorphic instances

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

2 total

Σ#PresentationMapping
82241⟨a, b, c | abab=1, acca=1⟩φ(a) = b, φ(b) = c, φ(c) = a
82249⟨a, b, c | abab=1, caac=1⟩φ(a) = b, φ(b) = c, φ(c) = a