YES

Problem:
 from(X) -> cons(X,n__from(n__s(X)))
 2ndspos(0(),Z) -> rnil()
 2ndspos(s(N),cons(X,n__cons(Y,Z))) -> rcons(posrecip(activate(Y)),2ndsneg(N,activate(Z)))
 2ndsneg(0(),Z) -> rnil()
 2ndsneg(s(N),cons(X,n__cons(Y,Z))) -> rcons(negrecip(activate(Y)),2ndspos(N,activate(Z)))
 pi(X) -> 2ndspos(X,from(0()))
 plus(0(),Y) -> Y
 plus(s(X),Y) -> s(plus(X,Y))
 times(0(),Y) -> 0()
 times(s(X),Y) -> plus(Y,times(X,Y))
 square(X) -> times(X,X)
 from(X) -> n__from(X)
 s(X) -> n__s(X)
 cons(X1,X2) -> n__cons(X1,X2)
 activate(n__from(X)) -> from(activate(X))
 activate(n__s(X)) -> s(activate(X))
 activate(n__cons(X1,X2)) -> cons(activate(X1),X2)
 activate(X) -> X

Proof:
 DP Processor:
  DPs:
   from#(X) -> cons#(X,n__from(n__s(X)))
   2ndspos#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Z)
   2ndspos#(s(N),cons(X,n__cons(Y,Z))) -> 2ndsneg#(N,activate(Z))
   2ndspos#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Y)
   2ndsneg#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Z)
   2ndsneg#(s(N),cons(X,n__cons(Y,Z))) -> 2ndspos#(N,activate(Z))
   2ndsneg#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Y)
   pi#(X) -> from#(0())
   pi#(X) -> 2ndspos#(X,from(0()))
   plus#(s(X),Y) -> plus#(X,Y)
   plus#(s(X),Y) -> s#(plus(X,Y))
   times#(s(X),Y) -> times#(X,Y)
   times#(s(X),Y) -> plus#(Y,times(X,Y))
   square#(X) -> times#(X,X)
   activate#(n__from(X)) -> activate#(X)
   activate#(n__from(X)) -> from#(activate(X))
   activate#(n__s(X)) -> activate#(X)
   activate#(n__s(X)) -> s#(activate(X))
   activate#(n__cons(X1,X2)) -> activate#(X1)
   activate#(n__cons(X1,X2)) -> cons#(activate(X1),X2)
  TRS:
   from(X) -> cons(X,n__from(n__s(X)))
   2ndspos(0(),Z) -> rnil()
   2ndspos(s(N),cons(X,n__cons(Y,Z))) -> rcons(posrecip(activate(Y)),2ndsneg(N,activate(Z)))
   2ndsneg(0(),Z) -> rnil()
   2ndsneg(s(N),cons(X,n__cons(Y,Z))) -> rcons(negrecip(activate(Y)),2ndspos(N,activate(Z)))
   pi(X) -> 2ndspos(X,from(0()))
   plus(0(),Y) -> Y
   plus(s(X),Y) -> s(plus(X,Y))
   times(0(),Y) -> 0()
   times(s(X),Y) -> plus(Y,times(X,Y))
   square(X) -> times(X,X)
   from(X) -> n__from(X)
   s(X) -> n__s(X)
   cons(X1,X2) -> n__cons(X1,X2)
   activate(n__from(X)) -> from(activate(X))
   activate(n__s(X)) -> s(activate(X))
   activate(n__cons(X1,X2)) -> cons(activate(X1),X2)
   activate(X) -> X
  Usable Rule Processor:
   DPs:
    from#(X) -> cons#(X,n__from(n__s(X)))
    2ndspos#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Z)
    2ndspos#(s(N),cons(X,n__cons(Y,Z))) -> 2ndsneg#(N,activate(Z))
    2ndspos#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Y)
    2ndsneg#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Z)
    2ndsneg#(s(N),cons(X,n__cons(Y,Z))) -> 2ndspos#(N,activate(Z))
    2ndsneg#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Y)
    pi#(X) -> from#(0())
    pi#(X) -> 2ndspos#(X,from(0()))
    plus#(s(X),Y) -> plus#(X,Y)
    plus#(s(X),Y) -> s#(plus(X,Y))
    times#(s(X),Y) -> times#(X,Y)
    times#(s(X),Y) -> plus#(Y,times(X,Y))
    square#(X) -> times#(X,X)
    activate#(n__from(X)) -> activate#(X)
    activate#(n__from(X)) -> from#(activate(X))
    activate#(n__s(X)) -> activate#(X)
    activate#(n__s(X)) -> s#(activate(X))
    activate#(n__cons(X1,X2)) -> activate#(X1)
    activate#(n__cons(X1,X2)) -> cons#(activate(X1),X2)
   TRS:
    activate(n__from(X)) -> from(activate(X))
    activate(n__s(X)) -> s(activate(X))
    activate(n__cons(X1,X2)) -> cons(activate(X1),X2)
    activate(X) -> X
    from(X) -> cons(X,n__from(n__s(X)))
    from(X) -> n__from(X)
    s(X) -> n__s(X)
    cons(X1,X2) -> n__cons(X1,X2)
    plus(0(),Y) -> Y
    plus(s(X),Y) -> s(plus(X,Y))
    times(0(),Y) -> 0()
    times(s(X),Y) -> plus(Y,times(X,Y))
   Matrix Interpretation Processor: dim=2
    
    usable rules:
     activate(n__from(X)) -> from(activate(X))
     activate(n__s(X)) -> s(activate(X))
     activate(n__cons(X1,X2)) -> cons(activate(X1),X2)
     activate(X) -> X
     from(X) -> cons(X,n__from(n__s(X)))
     from(X) -> n__from(X)
     s(X) -> n__s(X)
     cons(X1,X2) -> n__cons(X1,X2)
    interpretation:
     [square#](x0) = [3 2]x0 + [2],
     
     [times#](x0, x1) = [1 0]x0 + [2 0]x1 + [1],
     
     [s#](x0) = [0],
     
     [plus#](x0, x1) = [1 0]x0 + [1],
     
     [pi#](x0) = [3 1]x0 + [2],
     
     [2ndsneg#](x0, x1) = [3 0]x0 + [1 0]x1,
     
     [activate#](x0) = [1 0]x0 + [1],
     
     [2ndspos#](x0, x1) = [2 0]x0 + [1 0]x1,
     
     [cons#](x0, x1) = [0],
     
     [from#](x0) = [1],
     
                       [1 0]     [2 2]     [1]
     [times](x0, x1) = [0 2]x0 + [3 0]x1 + [3],
     
                      [0 2]     [1 1]     [2]
     [plus](x0, x1) = [0 1]x0 + [1 0]x1 + [2],
     
                      [1 0]  
     [activate](x0) = [3 1]x0,
     
                         [1 0]     [0 2]     [1]
     [n__cons](x0, x1) = [1 0]x0 + [1 1]x1 + [0],
     
               [2 0]     [2]
     [s](x0) = [0 0]x0 + [2],
     
           [0]
     [0] = [2],
     
                      [1 0]     [0 2]     [1]
     [cons](x0, x1) = [1 0]x0 + [1 2]x1 + [0],
     
                     [1 0]     [1]
     [n__from](x0) = [0 0]x0 + [0],
     
                  [2 0]     [2]
     [n__s](x0) = [0 0]x0 + [0],
     
                  [1 0]     [1]
     [from](x0) = [3 0]x0 + [3]
    orientation:
     from#(X) = [1] >= [0] = cons#(X,n__from(n__s(X)))
     
     2ndspos#(s(N),cons(X,n__cons(Y,Z))) = [4 0]N + [1 0]X + [2 0]Y + [2 2]Z + [5] >= [1 0]Z + [1] = activate#(Z)
     
     2ndspos#(s(N),cons(X,n__cons(Y,Z))) = [4 0]N + [1 0]X + [2 0]Y + [2 2]Z + [5] >= [3 0]N + [1 0]Z = 2ndsneg#(N,activate(Z))
     
     2ndspos#(s(N),cons(X,n__cons(Y,Z))) = [4 0]N + [1 0]X + [2 0]Y + [2 2]Z + [5] >= [1 0]Y + [1] = activate#(Y)
     
     2ndsneg#(s(N),cons(X,n__cons(Y,Z))) = [6 0]N + [1 0]X + [2 0]Y + [2 2]Z + [7] >= [1 0]Z + [1] = activate#(Z)
     
     2ndsneg#(s(N),cons(X,n__cons(Y,Z))) = [6 0]N + [1 0]X + [2 0]Y + [2 2]Z + [7] >= [2 0]N + [1 0]Z = 2ndspos#(N,activate(Z))
     
     2ndsneg#(s(N),cons(X,n__cons(Y,Z))) = [6 0]N + [1 0]X + [2 0]Y + [2 2]Z + [7] >= [1 0]Y + [1] = activate#(Y)
     
     pi#(X) = [3 1]X + [2] >= [1] = from#(0())
     
     pi#(X) = [3 1]X + [2] >= [2 0]X + [1] = 2ndspos#(X,from(0()))
     
     plus#(s(X),Y) = [2 0]X + [3] >= [1 0]X + [1] = plus#(X,Y)
     
     plus#(s(X),Y) = [2 0]X + [3] >= [0] = s#(plus(X,Y))
     
     times#(s(X),Y) = [2 0]X + [2 0]Y + [3] >= [1 0]X + [2 0]Y + [1] = times#(X,Y)
     
     times#(s(X),Y) = [2 0]X + [2 0]Y + [3] >= [1 0]Y + [1] = plus#(Y,times(X,Y))
     
     square#(X) = [3 2]X + [2] >= [3 0]X + [1] = times#(X,X)
     
     activate#(n__from(X)) = [1 0]X + [2] >= [1 0]X + [1] = activate#(X)
     
     activate#(n__from(X)) = [1 0]X + [2] >= [1] = from#(activate(X))
     
     activate#(n__s(X)) = [2 0]X + [3] >= [1 0]X + [1] = activate#(X)
     
     activate#(n__s(X)) = [2 0]X + [3] >= [0] = s#(activate(X))
     
     activate#(n__cons(X1,X2)) = [1 0]X1 + [0 2]X2 + [2] >= [1 0]X1 + [1] = activate#(X1)
     
     activate#(n__cons(X1,X2)) = [1 0]X1 + [0 2]X2 + [2] >= [0] = cons#(activate(X1),X2)
     
                            [1 0]    [1]    [1 0]    [1]                    
     activate(n__from(X)) = [3 0]X + [3] >= [3 0]X + [3] = from(activate(X))
     
                         [2 0]    [2]    [2 0]    [2]                 
     activate(n__s(X)) = [6 0]X + [6] >= [0 0]X + [2] = s(activate(X))
     
                                [1 0]     [0 2]     [1]    [1 0]     [0 2]     [1]                        
     activate(n__cons(X1,X2)) = [4 0]X1 + [1 7]X2 + [3] >= [1 0]X1 + [1 2]X2 + [0] = cons(activate(X1),X2)
     
                   [1 0]          
     activate(X) = [3 1]X >= X = X
     
               [1 0]    [1]    [1 0]    [1]                           
     from(X) = [3 0]X + [3] >= [3 0]X + [3] = cons(X,n__from(n__s(X)))
     
               [1 0]    [1]    [1 0]    [1]             
     from(X) = [3 0]X + [3] >= [0 0]X + [0] = n__from(X)
     
            [2 0]    [2]    [2 0]    [2]          
     s(X) = [0 0]X + [2] >= [0 0]X + [0] = n__s(X)
     
                   [1 0]     [0 2]     [1]    [1 0]     [0 2]     [1]                 
     cons(X1,X2) = [1 0]X1 + [1 2]X2 + [0] >= [1 0]X1 + [1 1]X2 + [0] = n__cons(X1,X2)
     
                   [1 1]    [6]         
     plus(0(),Y) = [1 0]Y + [4] >= Y = Y
     
                    [1 1]    [6]    [0 4]    [2 2]    [6]               
     plus(s(X),Y) = [1 0]Y + [4] >= [0 0]X + [0 0]Y + [2] = s(plus(X,Y))
     
                    [2 2]    [1]    [0]      
     times(0(),Y) = [3 0]Y + [7] >= [2] = 0()
     
                     [2 0]    [2 2]    [3]    [1 2]    [5 4]    [6]                     
     times(s(X),Y) = [0 0]X + [3 0]Y + [7] >= [1 0]X + [2 3]Y + [3] = plus(Y,times(X,Y))
    problem:
     DPs:
      
     TRS:
      activate(n__from(X)) -> from(activate(X))
      activate(n__s(X)) -> s(activate(X))
      activate(n__cons(X1,X2)) -> cons(activate(X1),X2)
      activate(X) -> X
      from(X) -> cons(X,n__from(n__s(X)))
      from(X) -> n__from(X)
      s(X) -> n__s(X)
      cons(X1,X2) -> n__cons(X1,X2)
      plus(0(),Y) -> Y
      plus(s(X),Y) -> s(plus(X,Y))
      times(0(),Y) -> 0()
      times(s(X),Y) -> plus(Y,times(X,Y))
    Qed