YES

Problem:
 and(true(),X) -> activate(X)
 and(false(),Y) -> false()
 if(true(),X,Y) -> activate(X)
 if(false(),X,Y) -> activate(Y)
 add(0(),X) -> activate(X)
 add(s(X),Y) -> s(n__add(activate(X),activate(Y)))
 first(0(),X) -> nil()
 first(s(X),cons(Y,Z)) -> cons(activate(Y),n__first(activate(X),activate(Z)))
 from(X) -> cons(activate(X),n__from(n__s(activate(X))))
 add(X1,X2) -> n__add(X1,X2)
 first(X1,X2) -> n__first(X1,X2)
 from(X) -> n__from(X)
 s(X) -> n__s(X)
 activate(n__add(X1,X2)) -> add(X1,X2)
 activate(n__first(X1,X2)) -> first(X1,X2)
 activate(n__from(X)) -> from(X)
 activate(n__s(X)) -> s(X)
 activate(X) -> X

Proof:
 DP Processor:
  DPs:
   and#(true(),X) -> activate#(X)
   if#(true(),X,Y) -> activate#(X)
   if#(false(),X,Y) -> activate#(Y)
   add#(0(),X) -> activate#(X)
   add#(s(X),Y) -> activate#(Y)
   add#(s(X),Y) -> activate#(X)
   add#(s(X),Y) -> s#(n__add(activate(X),activate(Y)))
   first#(s(X),cons(Y,Z)) -> activate#(Z)
   first#(s(X),cons(Y,Z)) -> activate#(X)
   first#(s(X),cons(Y,Z)) -> activate#(Y)
   from#(X) -> activate#(X)
   activate#(n__add(X1,X2)) -> add#(X1,X2)
   activate#(n__first(X1,X2)) -> first#(X1,X2)
   activate#(n__from(X)) -> from#(X)
   activate#(n__s(X)) -> s#(X)
  TRS:
   and(true(),X) -> activate(X)
   and(false(),Y) -> false()
   if(true(),X,Y) -> activate(X)
   if(false(),X,Y) -> activate(Y)
   add(0(),X) -> activate(X)
   add(s(X),Y) -> s(n__add(activate(X),activate(Y)))
   first(0(),X) -> nil()
   first(s(X),cons(Y,Z)) -> cons(activate(Y),n__first(activate(X),activate(Z)))
   from(X) -> cons(activate(X),n__from(n__s(activate(X))))
   add(X1,X2) -> n__add(X1,X2)
   first(X1,X2) -> n__first(X1,X2)
   from(X) -> n__from(X)
   s(X) -> n__s(X)
   activate(n__add(X1,X2)) -> add(X1,X2)
   activate(n__first(X1,X2)) -> first(X1,X2)
   activate(n__from(X)) -> from(X)
   activate(n__s(X)) -> s(X)
   activate(X) -> X
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [from#](x0) = 1/2x0 + 5/2,
    
    [first#](x0, x1) = 1/2x0 + x1 + 3/2,
    
    [s#](x0) = 1/2,
    
    [add#](x0, x1) = 1/2x0 + 1/2x1 + 5/2,
    
    [if#](x0, x1, x2) = 2x1 + 2x2 + 5/2,
    
    [activate#](x0) = 1/2x0 + 2,
    
    [and#](x0, x1) = 2x0 + 1/2x1 + 3/2,
    
    [n__from](x0) = 2x0 + 2,
    
    [n__s](x0) = x0,
    
    [from](x0) = 2x0 + 2,
    
    [n__first](x0, x1) = x0 + 2x1,
    
    [cons](x0, x1) = 1/2x0 + 1/2x1 + 1,
    
    [nil] = 3,
    
    [first](x0, x1) = x0 + 2x1,
    
    [n__add](x0, x1) = x0 + x1 + 2,
    
    [s](x0) = x0,
    
    [add](x0, x1) = x0 + x1 + 2,
    
    [0] = 3,
    
    [if](x0, x1, x2) = 3/2x1 + 3/2x2 + 2,
    
    [false] = 2,
    
    [activate](x0) = x0,
    
    [and](x0, x1) = 3/2x0 + 3/2x1 + 2,
    
    [true] = 1
   orientation:
    and#(true(),X) = 1/2X + 7/2 >= 1/2X + 2 = activate#(X)
    
    if#(true(),X,Y) = 2X + 2Y + 5/2 >= 1/2X + 2 = activate#(X)
    
    if#(false(),X,Y) = 2X + 2Y + 5/2 >= 1/2Y + 2 = activate#(Y)
    
    add#(0(),X) = 1/2X + 4 >= 1/2X + 2 = activate#(X)
    
    add#(s(X),Y) = 1/2X + 1/2Y + 5/2 >= 1/2Y + 2 = activate#(Y)
    
    add#(s(X),Y) = 1/2X + 1/2Y + 5/2 >= 1/2X + 2 = activate#(X)
    
    add#(s(X),Y) = 1/2X + 1/2Y + 5/2 >= 1/2 = s#(n__add(activate(X),activate(Y)))
    
    first#(s(X),cons(Y,Z)) = 1/2X + 1/2Y + 1/2Z + 5/2 >= 1/2Z + 2 = activate#(Z)
    
    first#(s(X),cons(Y,Z)) = 1/2X + 1/2Y + 1/2Z + 5/2 >= 1/2X + 2 = activate#(X)
    
    first#(s(X),cons(Y,Z)) = 1/2X + 1/2Y + 1/2Z + 5/2 >= 1/2Y + 2 = activate#(Y)
    
    from#(X) = 1/2X + 5/2 >= 1/2X + 2 = activate#(X)
    
    activate#(n__add(X1,X2)) = 1/2X1 + 1/2X2 + 3 >= 1/2X1 + 1/2X2 + 5/2 = add#(X1,X2)
    
    activate#(n__first(X1,X2)) = 1/2X1 + X2 + 2 >= 1/2X1 + X2 + 3/2 = first#(X1,X2)
    
    activate#(n__from(X)) = X + 3 >= 1/2X + 5/2 = from#(X)
    
    activate#(n__s(X)) = 1/2X + 2 >= 1/2 = s#(X)
    
    and(true(),X) = 3/2X + 7/2 >= X = activate(X)
    
    and(false(),Y) = 3/2Y + 5 >= 2 = false()
    
    if(true(),X,Y) = 3/2X + 3/2Y + 2 >= X = activate(X)
    
    if(false(),X,Y) = 3/2X + 3/2Y + 2 >= Y = activate(Y)
    
    add(0(),X) = X + 5 >= X = activate(X)
    
    add(s(X),Y) = X + Y + 2 >= X + Y + 2 = s(n__add(activate(X),activate(Y)))
    
    first(0(),X) = 2X + 3 >= 3 = nil()
    
    first(s(X),cons(Y,Z)) = X + Y + Z + 2 >= 1/2X + 1/2Y + Z + 1 = cons(activate(Y),n__first(activate(X),activate(Z)))
    
    from(X) = 2X + 2 >= 3/2X + 2 = cons(activate(X),n__from(n__s(activate(X))))
    
    add(X1,X2) = X1 + X2 + 2 >= X1 + X2 + 2 = n__add(X1,X2)
    
    first(X1,X2) = X1 + 2X2 >= X1 + 2X2 = n__first(X1,X2)
    
    from(X) = 2X + 2 >= 2X + 2 = n__from(X)
    
    s(X) = X >= X = n__s(X)
    
    activate(n__add(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = add(X1,X2)
    
    activate(n__first(X1,X2)) = X1 + 2X2 >= X1 + 2X2 = first(X1,X2)
    
    activate(n__from(X)) = 2X + 2 >= 2X + 2 = from(X)
    
    activate(n__s(X)) = X >= X = s(X)
    
    activate(X) = X >= X = X
   problem:
    DPs:
     
    TRS:
     and(true(),X) -> activate(X)
     and(false(),Y) -> false()
     if(true(),X,Y) -> activate(X)
     if(false(),X,Y) -> activate(Y)
     add(0(),X) -> activate(X)
     add(s(X),Y) -> s(n__add(activate(X),activate(Y)))
     first(0(),X) -> nil()
     first(s(X),cons(Y,Z)) -> cons(activate(Y),n__first(activate(X),activate(Z)))
     from(X) -> cons(activate(X),n__from(n__s(activate(X))))
     add(X1,X2) -> n__add(X1,X2)
     first(X1,X2) -> n__first(X1,X2)
     from(X) -> n__from(X)
     s(X) -> n__s(X)
     activate(n__add(X1,X2)) -> add(X1,X2)
     activate(n__first(X1,X2)) -> first(X1,X2)
     activate(n__from(X)) -> from(X)
     activate(n__s(X)) -> s(X)
     activate(X) -> X
   Qed