#2795 ⟨a, b | aaaaaabaaba=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. ca ⇒ ac [6]
2. cd ⇒ 1 [9]
3. da ⇒ ad [24]
4. dc ⇒ 1 [22]
5. a7 ⇒ c [2]
6. a2b ⇒ cba2d [10]
7. acb ⇒ dbac2 [45]
8. c2b ⇒ adba6c2 [39]
9. d2b ⇒ aba6d3 [33]
10. a2db ⇒ ba2d [27]
11. bcb ⇒ a5d [30]
# ab:aaaaaabaaba=1 acd/b aaaaaaa=c,baab=d magic:0
ca=ac
cd=1
da=ad
dc=1
aaaaaaa=c
aab=cbaad
acb=dbacc
ccb=adbaaaaaacc
ddb=abaaaaaaddd
aadb=baad
bcb=aaaaad

Isomorphic instances

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

4 total

Σ#PresentationMapping
112813⟨a, b | aaaaabaabaa=1⟩φ(a) = a, φ(b) = b
112847⟨a, b | aaaabaabaaa=1⟩φ(a) = a, φ(b) = b
113005⟨a, b | aabaaaaaaab=1⟩φ(a) = a, φ(b) = b
113170⟨a, b | abaaaaaaaba=1⟩φ(a) = a, φ(b) = b