YES

Problem:
 fst(0(),Z) -> nil()
 fst(s(X),cons(Y,Z)) -> cons(Y,n__fst(activate(X),activate(Z)))
 from(X) -> cons(X,n__from(s(X)))
 add(0(),X) -> X
 add(s(X),Y) -> s(n__add(activate(X),Y))
 len(nil()) -> 0()
 len(cons(X,Z)) -> s(n__len(activate(Z)))
 fst(X1,X2) -> n__fst(X1,X2)
 from(X) -> n__from(X)
 add(X1,X2) -> n__add(X1,X2)
 len(X) -> n__len(X)
 activate(n__fst(X1,X2)) -> fst(X1,X2)
 activate(n__from(X)) -> from(X)
 activate(n__add(X1,X2)) -> add(X1,X2)
 activate(n__len(X)) -> len(X)
 activate(X) -> X

Proof:
 DP Processor:
  DPs:
   fst#(s(X),cons(Y,Z)) -> activate#(Z)
   fst#(s(X),cons(Y,Z)) -> activate#(X)
   add#(s(X),Y) -> activate#(X)
   len#(cons(X,Z)) -> activate#(Z)
   activate#(n__fst(X1,X2)) -> fst#(X1,X2)
   activate#(n__from(X)) -> from#(X)
   activate#(n__add(X1,X2)) -> add#(X1,X2)
   activate#(n__len(X)) -> len#(X)
  TRS:
   fst(0(),Z) -> nil()
   fst(s(X),cons(Y,Z)) -> cons(Y,n__fst(activate(X),activate(Z)))
   from(X) -> cons(X,n__from(s(X)))
   add(0(),X) -> X
   add(s(X),Y) -> s(n__add(activate(X),Y))
   len(nil()) -> 0()
   len(cons(X,Z)) -> s(n__len(activate(Z)))
   fst(X1,X2) -> n__fst(X1,X2)
   from(X) -> n__from(X)
   add(X1,X2) -> n__add(X1,X2)
   len(X) -> n__len(X)
   activate(n__fst(X1,X2)) -> fst(X1,X2)
   activate(n__from(X)) -> from(X)
   activate(n__add(X1,X2)) -> add(X1,X2)
   activate(n__len(X)) -> len(X)
   activate(X) -> X
  Usable Rule Processor:
   DPs:
    fst#(s(X),cons(Y,Z)) -> activate#(Z)
    fst#(s(X),cons(Y,Z)) -> activate#(X)
    add#(s(X),Y) -> activate#(X)
    len#(cons(X,Z)) -> activate#(Z)
    activate#(n__fst(X1,X2)) -> fst#(X1,X2)
    activate#(n__from(X)) -> from#(X)
    activate#(n__add(X1,X2)) -> add#(X1,X2)
    activate#(n__len(X)) -> len#(X)
   TRS:
    
   Arctic Interpretation Processor:
    dimension: 1
    usable rules:
     
    interpretation:
     [len#](x0) = x0,
     
     [add#](x0, x1) = 1x0 + x1 + 0,
     
     [from#](x0) = x0 + 1,
     
     [activate#](x0) = x0,
     
     [fst#](x0, x1) = 1x0 + x1,
     
     [n__len](x0) = 1x0 + 4,
     
     [n__add](x0, x1) = 2x0 + 3x1 + 7,
     
     [n__from](x0) = 3x0 + 6,
     
     [n__fst](x0, x1) = 2x0 + 7x1 + 1,
     
     [cons](x0, x1) = 1x0 + 1x1 + 1,
     
     [s](x0) = 4x0
    orientation:
     fst#(s(X),cons(Y,Z)) = 5X + 1Y + 1Z + 1 >= Z = activate#(Z)
     
     fst#(s(X),cons(Y,Z)) = 5X + 1Y + 1Z + 1 >= X = activate#(X)
     
     add#(s(X),Y) = 5X + Y + 0 >= X = activate#(X)
     
     len#(cons(X,Z)) = 1X + 1Z + 1 >= Z = activate#(Z)
     
     activate#(n__fst(X1,X2)) = 2X1 + 7X2 + 1 >= 1X1 + X2 = fst#(X1,X2)
     
     activate#(n__from(X)) = 3X + 6 >= X + 1 = from#(X)
     
     activate#(n__add(X1,X2)) = 2X1 + 3X2 + 7 >= 1X1 + X2 + 0 = add#(X1,X2)
     
     activate#(n__len(X)) = 1X + 4 >= X = len#(X)
    problem:
     DPs:
      
     TRS:
      
    Qed