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(s(X)))
 first(X1,X2) -> n__first(X1,X2)
 from(X) -> n__from(X)
 activate(n__first(X1,X2)) -> first(X1,X2)
 activate(n__from(X)) -> from(X)
 activate(X) -> X

Proof:
 DP Processor:
  DPs:
   first#(s(X),cons(Y,Z)) -> activate#(Z)
   activate#(n__first(X1,X2)) -> first#(X1,X2)
   activate#(n__from(X)) -> from#(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(s(X)))
   first(X1,X2) -> n__first(X1,X2)
   from(X) -> n__from(X)
   activate(n__first(X1,X2)) -> first(X1,X2)
   activate(n__from(X)) -> from(X)
   activate(X) -> X
  Usable Rule Processor:
   DPs:
    first#(s(X),cons(Y,Z)) -> activate#(Z)
    activate#(n__first(X1,X2)) -> first#(X1,X2)
    activate#(n__from(X)) -> from#(X)
   TRS:
    
   Arctic Interpretation Processor:
    dimension: 1
    usable rules:
     
    interpretation:
     [from#](x0) = x0 + -12,
     
     [activate#](x0) = 4x0,
     
     [first#](x0, x1) = -16x0 + x1 + -14,
     
     [n__from](x0) = 1x0 + 2,
     
     [n__first](x0, x1) = -11x0 + x1 + 0,
     
     [cons](x0, x1) = x0 + 7x1 + 0,
     
     [s](x0) = 4x0 + 10
    orientation:
     first#(s(X),cons(Y,Z)) = -12X + Y + 7Z + 0 >= 4Z = activate#(Z)
     
     activate#(n__first(X1,X2)) = -7X1 + 4X2 + 4 >= -16X1 + X2 + -14 = first#(X1,X2)
     
     activate#(n__from(X)) = 5X + 6 >= X + -12 = from#(X)
    problem:
     DPs:
      
     TRS:
      
    Qed