#2936 ⟨a, b | aaababababa=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. ac ⇒ ca [5]
2. a4 ⇒ c [2]
3. dc ⇒ 1 [19]
4. cd ⇒ 1 [16]
5. ad ⇒ da [20]
6. ab ⇒ cbda [23]
7. c3b ⇒ bc3 [30]
8. db ⇒ c2bd3 [27]
9. b(cb)3 ⇒ ca [32]
# ab:aaababababa=1 ca/d/b aaaa=c,bababab=d magic:0
ac=ca
aaaa=c
dc=1
cd=1
ad=da
ab=cbda
cccb=bccc
db=ccbddd
bcbcbcb=ca

Isomorphic instances

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

4 total

Σ#PresentationMapping
113066⟨a, b | aababababaa=1⟩φ(a) = a, φ(b) = b
113179⟨a, b | abaaaababab=1⟩φ(a) = a, φ(b) = b
113228⟨a, b | ababaaaabab=1⟩φ(a) = a, φ(b) = b
113239⟨a, b | abababaaaab=1⟩φ(a) = a, φ(b) = b