YES

Problem:
 a__first(0(),X) -> nil()
 a__first(s(X),cons(Y,Z)) -> cons(mark(Y),first(X,Z))
 a__from(X) -> cons(mark(X),from(s(X)))
 mark(first(X1,X2)) -> a__first(mark(X1),mark(X2))
 mark(from(X)) -> a__from(mark(X))
 mark(0()) -> 0()
 mark(nil()) -> nil()
 mark(s(X)) -> s(mark(X))
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 a__first(X1,X2) -> first(X1,X2)
 a__from(X) -> from(X)

Proof:
 DP Processor:
  DPs:
   a__first#(s(X),cons(Y,Z)) -> mark#(Y)
   a__from#(X) -> mark#(X)
   mark#(first(X1,X2)) -> mark#(X2)
   mark#(first(X1,X2)) -> mark#(X1)
   mark#(first(X1,X2)) -> a__first#(mark(X1),mark(X2))
   mark#(from(X)) -> mark#(X)
   mark#(from(X)) -> a__from#(mark(X))
   mark#(s(X)) -> mark#(X)
   mark#(cons(X1,X2)) -> mark#(X1)
  TRS:
   a__first(0(),X) -> nil()
   a__first(s(X),cons(Y,Z)) -> cons(mark(Y),first(X,Z))
   a__from(X) -> cons(mark(X),from(s(X)))
   mark(first(X1,X2)) -> a__first(mark(X1),mark(X2))
   mark(from(X)) -> a__from(mark(X))
   mark(0()) -> 0()
   mark(nil()) -> nil()
   mark(s(X)) -> s(mark(X))
   mark(cons(X1,X2)) -> cons(mark(X1),X2)
   a__first(X1,X2) -> first(X1,X2)
   a__from(X) -> from(X)
  Matrix Interpretation Processor: dim=1
   
   usable rules:
    a__first(0(),X) -> nil()
    a__first(s(X),cons(Y,Z)) -> cons(mark(Y),first(X,Z))
    a__from(X) -> cons(mark(X),from(s(X)))
    mark(first(X1,X2)) -> a__first(mark(X1),mark(X2))
    mark(from(X)) -> a__from(mark(X))
    mark(0()) -> 0()
    mark(nil()) -> nil()
    mark(s(X)) -> s(mark(X))
    mark(cons(X1,X2)) -> cons(mark(X1),X2)
    a__first(X1,X2) -> first(X1,X2)
    a__from(X) -> from(X)
   interpretation:
    [a__from#](x0) = 3/2x0 + 1,
    
    [mark#](x0) = x0 + 1/2,
    
    [a__first#](x0, x1) = 1/2x0 + x1,
    
    [from](x0) = 5/2x0 + 1,
    
    [a__from](x0) = 5/2x0 + 1,
    
    [first](x0, x1) = x0 + x1 + 2,
    
    [mark](x0) = x0,
    
    [cons](x0, x1) = 2x0 + 1/2,
    
    [s](x0) = 2x0 + 2,
    
    [nil] = 0,
    
    [a__first](x0, x1) = x0 + x1 + 2,
    
    [0] = 3
   orientation:
    a__first#(s(X),cons(Y,Z)) = X + 2Y + 3/2 >= Y + 1/2 = mark#(Y)
    
    a__from#(X) = 3/2X + 1 >= X + 1/2 = mark#(X)
    
    mark#(first(X1,X2)) = X1 + X2 + 5/2 >= X2 + 1/2 = mark#(X2)
    
    mark#(first(X1,X2)) = X1 + X2 + 5/2 >= X1 + 1/2 = mark#(X1)
    
    mark#(first(X1,X2)) = X1 + X2 + 5/2 >= 1/2X1 + X2 = a__first#(mark(X1),mark(X2))
    
    mark#(from(X)) = 5/2X + 3/2 >= X + 1/2 = mark#(X)
    
    mark#(from(X)) = 5/2X + 3/2 >= 3/2X + 1 = a__from#(mark(X))
    
    mark#(s(X)) = 2X + 5/2 >= X + 1/2 = mark#(X)
    
    mark#(cons(X1,X2)) = 2X1 + 1 >= X1 + 1/2 = mark#(X1)
    
    a__first(0(),X) = X + 5 >= 0 = nil()
    
    a__first(s(X),cons(Y,Z)) = 2X + 2Y + 9/2 >= 2Y + 1/2 = cons(mark(Y),first(X,Z))
    
    a__from(X) = 5/2X + 1 >= 2X + 1/2 = cons(mark(X),from(s(X)))
    
    mark(first(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = a__first(mark(X1),mark(X2))
    
    mark(from(X)) = 5/2X + 1 >= 5/2X + 1 = a__from(mark(X))
    
    mark(0()) = 3 >= 3 = 0()
    
    mark(nil()) = 0 >= 0 = nil()
    
    mark(s(X)) = 2X + 2 >= 2X + 2 = s(mark(X))
    
    mark(cons(X1,X2)) = 2X1 + 1/2 >= 2X1 + 1/2 = cons(mark(X1),X2)
    
    a__first(X1,X2) = X1 + X2 + 2 >= X1 + X2 + 2 = first(X1,X2)
    
    a__from(X) = 5/2X + 1 >= 5/2X + 1 = from(X)
   problem:
    DPs:
     
    TRS:
     a__first(0(),X) -> nil()
     a__first(s(X),cons(Y,Z)) -> cons(mark(Y),first(X,Z))
     a__from(X) -> cons(mark(X),from(s(X)))
     mark(first(X1,X2)) -> a__first(mark(X1),mark(X2))
     mark(from(X)) -> a__from(mark(X))
     mark(0()) -> 0()
     mark(nil()) -> nil()
     mark(s(X)) -> s(mark(X))
     mark(cons(X1,X2)) -> cons(mark(X1),X2)
     a__first(X1,X2) -> first(X1,X2)
     a__from(X) -> from(X)
   Qed