YES

Problem:
 from(X) -> cons(X,n__from(s(X)))
 2ndspos(0(),Z) -> rnil()
 2ndspos(s(N),cons(X,Z)) -> 2ndspos(s(N),cons2(X,activate(Z)))
 2ndspos(s(N),cons2(X,cons(Y,Z))) -> rcons(posrecip(Y),2ndsneg(N,activate(Z)))
 2ndsneg(0(),Z) -> rnil()
 2ndsneg(s(N),cons(X,Z)) -> 2ndsneg(s(N),cons2(X,activate(Z)))
 2ndsneg(s(N),cons2(X,cons(Y,Z))) -> rcons(negrecip(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)
 activate(n__from(X)) -> from(X)
 activate(X) -> X

Proof:
 DP Processor:
  DPs:
   2ndspos#(s(N),cons(X,Z)) -> activate#(Z)
   2ndspos#(s(N),cons(X,Z)) -> 2ndspos#(s(N),cons2(X,activate(Z)))
   2ndspos#(s(N),cons2(X,cons(Y,Z))) -> activate#(Z)
   2ndspos#(s(N),cons2(X,cons(Y,Z))) -> 2ndsneg#(N,activate(Z))
   2ndsneg#(s(N),cons(X,Z)) -> activate#(Z)
   2ndsneg#(s(N),cons(X,Z)) -> 2ndsneg#(s(N),cons2(X,activate(Z)))
   2ndsneg#(s(N),cons2(X,cons(Y,Z))) -> activate#(Z)
   2ndsneg#(s(N),cons2(X,cons(Y,Z))) -> 2ndspos#(N,activate(Z))
   pi#(X) -> from#(0())
   pi#(X) -> 2ndspos#(X,from(0()))
   plus#(s(X),Y) -> 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)) -> from#(X)
  TRS:
   from(X) -> cons(X,n__from(s(X)))
   2ndspos(0(),Z) -> rnil()
   2ndspos(s(N),cons(X,Z)) -> 2ndspos(s(N),cons2(X,activate(Z)))
   2ndspos(s(N),cons2(X,cons(Y,Z))) -> rcons(posrecip(Y),2ndsneg(N,activate(Z)))
   2ndsneg(0(),Z) -> rnil()
   2ndsneg(s(N),cons(X,Z)) -> 2ndsneg(s(N),cons2(X,activate(Z)))
   2ndsneg(s(N),cons2(X,cons(Y,Z))) -> rcons(negrecip(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)
   activate(n__from(X)) -> from(X)
   activate(X) -> X
  Usable Rule Processor:
   DPs:
    2ndspos#(s(N),cons(X,Z)) -> activate#(Z)
    2ndspos#(s(N),cons(X,Z)) -> 2ndspos#(s(N),cons2(X,activate(Z)))
    2ndspos#(s(N),cons2(X,cons(Y,Z))) -> activate#(Z)
    2ndspos#(s(N),cons2(X,cons(Y,Z))) -> 2ndsneg#(N,activate(Z))
    2ndsneg#(s(N),cons(X,Z)) -> activate#(Z)
    2ndsneg#(s(N),cons(X,Z)) -> 2ndsneg#(s(N),cons2(X,activate(Z)))
    2ndsneg#(s(N),cons2(X,cons(Y,Z))) -> activate#(Z)
    2ndsneg#(s(N),cons2(X,cons(Y,Z))) -> 2ndspos#(N,activate(Z))
    pi#(X) -> from#(0())
    pi#(X) -> 2ndspos#(X,from(0()))
    plus#(s(X),Y) -> 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)) -> from#(X)
   TRS:
    activate(n__from(X)) -> from(X)
    activate(X) -> X
    from(X) -> cons(X,n__from(s(X)))
    from(X) -> n__from(X)
    times(0(),Y) -> 0()
    times(s(X),Y) -> plus(Y,times(X,Y))
    plus(0(),Y) -> Y
    plus(s(X),Y) -> s(plus(X,Y))
   Matrix Interpretation Processor: dim=1
    
    usable rules:
     activate(n__from(X)) -> from(X)
     activate(X) -> X
     from(X) -> cons(X,n__from(s(X)))
     from(X) -> n__from(X)
    interpretation:
     [square#](x0) = 7/2x0 + 5/2,
     
     [times#](x0, x1) = 3/2x0 + 2x1 + 2,
     
     [plus#](x0, x1) = 3/2x0 + 1,
     
     [pi#](x0) = 3x0 + 2,
     
     [2ndsneg#](x0, x1) = 3/2x0 + x1,
     
     [activate#](x0) = 1/2,
     
     [2ndspos#](x0, x1) = 5/2x0 + x1 + 1/2,
     
     [from#](x0) = 0,
     
     [times](x0, x1) = 2,
     
     [plus](x0, x1) = 0,
     
     [cons2](x0, x1) = 1/2x1,
     
     [activate](x0) = x0 + 1,
     
     [0] = 0,
     
     [cons](x0, x1) = 2x1 + 1,
     
     [n__from](x0) = 0,
     
     [s](x0) = 2x0 + 3,
     
     [from](x0) = 1
    orientation:
     2ndspos#(s(N),cons(X,Z)) = 5N + 2Z + 9 >= 1/2 = activate#(Z)
     
     2ndspos#(s(N),cons(X,Z)) = 5N + 2Z + 9 >= 5N + 1/2Z + 17/2 = 2ndspos#(s(N),cons2(X,activate(Z)))
     
     2ndspos#(s(N),cons2(X,cons(Y,Z))) = 5N + Z + 17/2 >= 1/2 = activate#(Z)
     
     2ndspos#(s(N),cons2(X,cons(Y,Z))) = 5N + Z + 17/2 >= 3/2N + Z + 1 = 2ndsneg#(N,activate(Z))
     
     2ndsneg#(s(N),cons(X,Z)) = 3N + 2Z + 11/2 >= 1/2 = activate#(Z)
     
     2ndsneg#(s(N),cons(X,Z)) = 3N + 2Z + 11/2 >= 3N + 1/2Z + 5 = 2ndsneg#(s(N),cons2(X,activate(Z)))
     
     2ndsneg#(s(N),cons2(X,cons(Y,Z))) = 3N + Z + 5 >= 1/2 = activate#(Z)
     
     2ndsneg#(s(N),cons2(X,cons(Y,Z))) = 3N + Z + 5 >= 5/2N + Z + 3/2 = 2ndspos#(N,activate(Z))
     
     pi#(X) = 3X + 2 >= 0 = from#(0())
     
     pi#(X) = 3X + 2 >= 5/2X + 3/2 = 2ndspos#(X,from(0()))
     
     plus#(s(X),Y) = 3X + 11/2 >= 3/2X + 1 = plus#(X,Y)
     
     times#(s(X),Y) = 3X + 2Y + 13/2 >= 3/2X + 2Y + 2 = times#(X,Y)
     
     times#(s(X),Y) = 3X + 2Y + 13/2 >= 3/2Y + 1 = plus#(Y,times(X,Y))
     
     square#(X) = 7/2X + 5/2 >= 7/2X + 2 = times#(X,X)
     
     activate#(n__from(X)) = 1/2 >= 0 = from#(X)
     
     activate(n__from(X)) = 1 >= 1 = from(X)
     
     activate(X) = X + 1 >= X = X
     
     from(X) = 1 >= 1 = cons(X,n__from(s(X)))
     
     from(X) = 1 >= 0 = n__from(X)
     
     times(0(),Y) = 2 >= 0 = 0()
     
     times(s(X),Y) = 2 >= 0 = plus(Y,times(X,Y))
     
     plus(0(),Y) = 0 >= Y = Y
     
     plus(s(X),Y) = 0 >= 3 = s(plus(X,Y))
    problem:
     DPs:
      
     TRS:
      activate(n__from(X)) -> from(X)
      activate(X) -> X
      from(X) -> cons(X,n__from(s(X)))
      from(X) -> n__from(X)
      times(0(),Y) -> 0()
      times(s(X),Y) -> plus(Y,times(X,Y))
      plus(0(),Y) -> Y
      plus(s(X),Y) -> s(plus(X,Y))
    Qed