#2819 ⟨a, b | aaaaabababa=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 [6]
2. a6 ⇒ c [2]
3. dc ⇒ 1 [22]
4. cd ⇒ 1 [15]
5. ad ⇒ da [23]
6. ab ⇒ cbda [24]
7. c5b ⇒ bc5 [34]
8. db ⇒ c4bd5 [28]
9. b(cb)2 ⇒ a4 [29]
# ab:aaaaabababa=1 ca/d/b aaaaaa=c,babab=d magic:0
ac=ca
aaaaaa=c
dc=1
cd=1
ad=da
ab=cbda
cccccb=bccccc
db=ccccbddddd
bcbcb=aaaa

Isomorphic instances

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

3 total

Σ#PresentationMapping
112859⟨a, b | aaaabababaa=1⟩φ(a) = a, φ(b) = b
112934⟨a, b | aaabababaaa=1⟩φ(a) = a, φ(b) = b
113171⟨a, b | abaaaaaabab=1⟩φ(a) = a, φ(b) = b