YES

Problem:
 from(X) -> cons(X,n__from(s(X)))
 head(cons(X,XS)) -> X
 2nd(cons(X,XS)) -> head(activate(XS))
 take(0(),XS) -> nil()
 take(s(N),cons(X,XS)) -> cons(X,n__take(N,activate(XS)))
 sel(0(),cons(X,XS)) -> X
 sel(s(N),cons(X,XS)) -> sel(N,activate(XS))
 from(X) -> n__from(X)
 take(X1,X2) -> n__take(X1,X2)
 activate(n__from(X)) -> from(X)
 activate(n__take(X1,X2)) -> take(X1,X2)
 activate(X) -> X

Proof:
 DP Processor:
  DPs:
   2nd#(cons(X,XS)) -> activate#(XS)
   2nd#(cons(X,XS)) -> head#(activate(XS))
   take#(s(N),cons(X,XS)) -> activate#(XS)
   sel#(s(N),cons(X,XS)) -> activate#(XS)
   sel#(s(N),cons(X,XS)) -> sel#(N,activate(XS))
   activate#(n__from(X)) -> from#(X)
   activate#(n__take(X1,X2)) -> take#(X1,X2)
  TRS:
   from(X) -> cons(X,n__from(s(X)))
   head(cons(X,XS)) -> X
   2nd(cons(X,XS)) -> head(activate(XS))
   take(0(),XS) -> nil()
   take(s(N),cons(X,XS)) -> cons(X,n__take(N,activate(XS)))
   sel(0(),cons(X,XS)) -> X
   sel(s(N),cons(X,XS)) -> sel(N,activate(XS))
   from(X) -> n__from(X)
   take(X1,X2) -> n__take(X1,X2)
   activate(n__from(X)) -> from(X)
   activate(n__take(X1,X2)) -> take(X1,X2)
   activate(X) -> X
  Usable Rule Processor:
   DPs:
    2nd#(cons(X,XS)) -> activate#(XS)
    2nd#(cons(X,XS)) -> head#(activate(XS))
    take#(s(N),cons(X,XS)) -> activate#(XS)
    sel#(s(N),cons(X,XS)) -> activate#(XS)
    sel#(s(N),cons(X,XS)) -> sel#(N,activate(XS))
    activate#(n__from(X)) -> from#(X)
    activate#(n__take(X1,X2)) -> take#(X1,X2)
   TRS:
    activate(n__from(X)) -> from(X)
    activate(n__take(X1,X2)) -> take(X1,X2)
    activate(X) -> X
    from(X) -> cons(X,n__from(s(X)))
    from(X) -> n__from(X)
    take(0(),XS) -> nil()
    take(s(N),cons(X,XS)) -> cons(X,n__take(N,activate(XS)))
    take(X1,X2) -> n__take(X1,X2)
   Matrix Interpretation Processor: dim=1
    
    usable rules:
     activate(n__from(X)) -> from(X)
     activate(n__take(X1,X2)) -> take(X1,X2)
     activate(X) -> X
     from(X) -> cons(X,n__from(s(X)))
     from(X) -> n__from(X)
     take(0(),XS) -> nil()
     take(s(N),cons(X,XS)) -> cons(X,n__take(N,activate(XS)))
     take(X1,X2) -> n__take(X1,X2)
    interpretation:
     [sel#](x0, x1) = x0 + 4x1,
     
     [take#](x0, x1) = x1 + 4,
     
     [activate#](x0) = x0 + 4,
     
     [2nd#](x0) = 4x0 + 5,
     
     [head#](x0) = 4x0 + 4,
     
     [from#](x0) = 0,
     
     [n__take](x0, x1) = 4x1 + 1,
     
     [nil] = 0,
     
     [take](x0, x1) = 4x1 + 4,
     
     [0] = 0,
     
     [activate](x0) = x0 + 3,
     
     [cons](x0, x1) = x1 + 3,
     
     [n__from](x0) = 0,
     
     [s](x0) = x0 + 4,
     
     [from](x0) = 3
    orientation:
     2nd#(cons(X,XS)) = 4XS + 17 >= XS + 4 = activate#(XS)
     
     2nd#(cons(X,XS)) = 4XS + 17 >= 4XS + 16 = head#(activate(XS))
     
     take#(s(N),cons(X,XS)) = XS + 7 >= XS + 4 = activate#(XS)
     
     sel#(s(N),cons(X,XS)) = N + 4XS + 16 >= XS + 4 = activate#(XS)
     
     sel#(s(N),cons(X,XS)) = N + 4XS + 16 >= N + 4XS + 12 = sel#(N,activate(XS))
     
     activate#(n__from(X)) = 4 >= 0 = from#(X)
     
     activate#(n__take(X1,X2)) = 4X2 + 5 >= X2 + 4 = take#(X1,X2)
     
     activate(n__from(X)) = 3 >= 3 = from(X)
     
     activate(n__take(X1,X2)) = 4X2 + 4 >= 4X2 + 4 = take(X1,X2)
     
     activate(X) = X + 3 >= X = X
     
     from(X) = 3 >= 3 = cons(X,n__from(s(X)))
     
     from(X) = 3 >= 0 = n__from(X)
     
     take(0(),XS) = 4XS + 4 >= 0 = nil()
     
     take(s(N),cons(X,XS)) = 4XS + 16 >= 4XS + 16 = cons(X,n__take(N,activate(XS)))
     
     take(X1,X2) = 4X2 + 4 >= 4X2 + 1 = n__take(X1,X2)
    problem:
     DPs:
      
     TRS:
      activate(n__from(X)) -> from(X)
      activate(n__take(X1,X2)) -> take(X1,X2)
      activate(X) -> X
      from(X) -> cons(X,n__from(s(X)))
      from(X) -> n__from(X)
      take(0(),XS) -> nil()
      take(s(N),cons(X,XS)) -> cons(X,n__take(N,activate(XS)))
      take(X1,X2) -> n__take(X1,X2)
    Qed