YES

Problem:
 first(0(),X) -> nil()
 first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z)))
 from(X) -> cons(X,n__from(n__s(X)))
 first(X1,X2) -> n__first(X1,X2)
 from(X) -> n__from(X)
 s(X) -> n__s(X)
 activate(n__first(X1,X2)) -> first(activate(X1),activate(X2))
 activate(n__from(X)) -> from(activate(X))
 activate(n__s(X)) -> s(activate(X))
 activate(X) -> X

Proof:
 DP Processor:
  DPs:
   first#(s(X),cons(Y,Z)) -> activate#(Z)
   activate#(n__first(X1,X2)) -> activate#(X2)
   activate#(n__first(X1,X2)) -> activate#(X1)
   activate#(n__first(X1,X2)) -> first#(activate(X1),activate(X2))
   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))
  TRS:
   first(0(),X) -> nil()
   first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z)))
   from(X) -> cons(X,n__from(n__s(X)))
   first(X1,X2) -> n__first(X1,X2)
   from(X) -> n__from(X)
   s(X) -> n__s(X)
   activate(n__first(X1,X2)) -> first(activate(X1),activate(X2))
   activate(n__from(X)) -> from(activate(X))
   activate(n__s(X)) -> s(activate(X))
   activate(X) -> X
  Matrix Interpretation Processor: dim=1
   
   usable rules:
    first(0(),X) -> nil()
    first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z)))
    from(X) -> cons(X,n__from(n__s(X)))
    first(X1,X2) -> n__first(X1,X2)
    from(X) -> n__from(X)
    s(X) -> n__s(X)
    activate(n__first(X1,X2)) -> first(activate(X1),activate(X2))
    activate(n__from(X)) -> from(activate(X))
    activate(n__s(X)) -> s(activate(X))
    activate(X) -> X
   interpretation:
    [s#](x0) = 0,
    
    [from#](x0) = 1,
    
    [activate#](x0) = 1/2x0,
    
    [first#](x0, x1) = x1,
    
    [n__from](x0) = x0 + 3,
    
    [n__s](x0) = x0 + 2,
    
    [from](x0) = x0 + 3,
    
    [n__first](x0, x1) = 2x0 + 2x1 + 1,
    
    [activate](x0) = x0,
    
    [cons](x0, x1) = 1/2x1 + 1/2,
    
    [s](x0) = x0 + 2,
    
    [nil] = 0,
    
    [first](x0, x1) = 2x0 + 2x1 + 1,
    
    [0] = 7/2
   orientation:
    first#(s(X),cons(Y,Z)) = 1/2Z + 1/2 >= 1/2Z = activate#(Z)
    
    activate#(n__first(X1,X2)) = X1 + X2 + 1/2 >= 1/2X2 = activate#(X2)
    
    activate#(n__first(X1,X2)) = X1 + X2 + 1/2 >= 1/2X1 = activate#(X1)
    
    activate#(n__first(X1,X2)) = X1 + X2 + 1/2 >= X2 = first#(activate(X1),activate(X2))
    
    activate#(n__from(X)) = 1/2X + 3/2 >= 1/2X = activate#(X)
    
    activate#(n__from(X)) = 1/2X + 3/2 >= 1 = from#(activate(X))
    
    activate#(n__s(X)) = 1/2X + 1 >= 1/2X = activate#(X)
    
    activate#(n__s(X)) = 1/2X + 1 >= 0 = s#(activate(X))
    
    first(0(),X) = 2X + 8 >= 0 = nil()
    
    first(s(X),cons(Y,Z)) = 2X + Z + 6 >= X + Z + 1 = cons(Y,n__first(X,activate(Z)))
    
    from(X) = X + 3 >= 1/2X + 3 = cons(X,n__from(n__s(X)))
    
    first(X1,X2) = 2X1 + 2X2 + 1 >= 2X1 + 2X2 + 1 = n__first(X1,X2)
    
    from(X) = X + 3 >= X + 3 = n__from(X)
    
    s(X) = X + 2 >= X + 2 = n__s(X)
    
    activate(n__first(X1,X2)) = 2X1 + 2X2 + 1 >= 2X1 + 2X2 + 1 = first(activate(X1),activate(X2))
    
    activate(n__from(X)) = X + 3 >= X + 3 = from(activate(X))
    
    activate(n__s(X)) = X + 2 >= X + 2 = s(activate(X))
    
    activate(X) = X >= X = X
   problem:
    DPs:
     
    TRS:
     first(0(),X) -> nil()
     first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z)))
     from(X) -> cons(X,n__from(n__s(X)))
     first(X1,X2) -> n__first(X1,X2)
     from(X) -> n__from(X)
     s(X) -> n__s(X)
     activate(n__first(X1,X2)) -> first(activate(X1),activate(X2))
     activate(n__from(X)) -> from(activate(X))
     activate(n__s(X)) -> s(activate(X))
     activate(X) -> X
   Qed