#2787 ⟨a, b | aaaaaaababa=1⟩

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  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. a8 ⇒ c [2]
3. dc ⇒ 1 [26]
4. cd ⇒ 1 [14]
5. ad ⇒ da [25]
6. ab ⇒ cbda [32]
7. c7b ⇒ bc7 [39]
8. db ⇒ c6bd7 [30]
9. bcb ⇒ da7 [29]
# ab:aaaaaaababa=1 ca/d/b aaaaaaaa=c,bab=d magic:0
ac=ca
aaaaaaaa=c
dc=1
cd=1
ad=da
ab=cbda
cccccccb=bccccccc
db=ccccccbddddddd
bcb=daaaaaaa

Isomorphic instances

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

4 total

Σ#PresentationMapping
112797⟨a, b | aaaaaababaa=1⟩φ(a) = a, φ(b) = b
112817⟨a, b | aaaaababaaa=1⟩φ(a) = a, φ(b) = b
112855⟨a, b | aaaababaaaa=1⟩φ(a) = a, φ(b) = b
113169⟨a, b | abaaaaaaaab=1⟩φ(a) = a, φ(b) = b