YES

Problem:
 a__and(true(),X) -> mark(X)
 a__and(false(),Y) -> false()
 a__if(true(),X,Y) -> mark(X)
 a__if(false(),X,Y) -> mark(Y)
 a__add(0(),X) -> mark(X)
 a__add(s(X),Y) -> s(add(X,Y))
 a__first(0(),X) -> nil()
 a__first(s(X),cons(Y,Z)) -> cons(Y,first(X,Z))
 a__from(X) -> cons(X,from(s(X)))
 mark(and(X1,X2)) -> a__and(mark(X1),X2)
 mark(if(X1,X2,X3)) -> a__if(mark(X1),X2,X3)
 mark(add(X1,X2)) -> a__add(mark(X1),X2)
 mark(first(X1,X2)) -> a__first(mark(X1),mark(X2))
 mark(from(X)) -> a__from(X)
 mark(true()) -> true()
 mark(false()) -> false()
 mark(0()) -> 0()
 mark(s(X)) -> s(X)
 mark(nil()) -> nil()
 mark(cons(X1,X2)) -> cons(X1,X2)
 a__and(X1,X2) -> and(X1,X2)
 a__if(X1,X2,X3) -> if(X1,X2,X3)
 a__add(X1,X2) -> add(X1,X2)
 a__first(X1,X2) -> first(X1,X2)
 a__from(X) -> from(X)

Proof:
 DP Processor:
  DPs:
   a__and#(true(),X) -> mark#(X)
   a__if#(true(),X,Y) -> mark#(X)
   a__if#(false(),X,Y) -> mark#(Y)
   a__add#(0(),X) -> mark#(X)
   mark#(and(X1,X2)) -> mark#(X1)
   mark#(and(X1,X2)) -> a__and#(mark(X1),X2)
   mark#(if(X1,X2,X3)) -> mark#(X1)
   mark#(if(X1,X2,X3)) -> a__if#(mark(X1),X2,X3)
   mark#(add(X1,X2)) -> mark#(X1)
   mark#(add(X1,X2)) -> a__add#(mark(X1),X2)
   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)) -> a__from#(X)
  TRS:
   a__and(true(),X) -> mark(X)
   a__and(false(),Y) -> false()
   a__if(true(),X,Y) -> mark(X)
   a__if(false(),X,Y) -> mark(Y)
   a__add(0(),X) -> mark(X)
   a__add(s(X),Y) -> s(add(X,Y))
   a__first(0(),X) -> nil()
   a__first(s(X),cons(Y,Z)) -> cons(Y,first(X,Z))
   a__from(X) -> cons(X,from(s(X)))
   mark(and(X1,X2)) -> a__and(mark(X1),X2)
   mark(if(X1,X2,X3)) -> a__if(mark(X1),X2,X3)
   mark(add(X1,X2)) -> a__add(mark(X1),X2)
   mark(first(X1,X2)) -> a__first(mark(X1),mark(X2))
   mark(from(X)) -> a__from(X)
   mark(true()) -> true()
   mark(false()) -> false()
   mark(0()) -> 0()
   mark(s(X)) -> s(X)
   mark(nil()) -> nil()
   mark(cons(X1,X2)) -> cons(X1,X2)
   a__and(X1,X2) -> and(X1,X2)
   a__if(X1,X2,X3) -> if(X1,X2,X3)
   a__add(X1,X2) -> add(X1,X2)
   a__first(X1,X2) -> first(X1,X2)
   a__from(X) -> from(X)
  TDG Processor:
   DPs:
    a__and#(true(),X) -> mark#(X)
    a__if#(true(),X,Y) -> mark#(X)
    a__if#(false(),X,Y) -> mark#(Y)
    a__add#(0(),X) -> mark#(X)
    mark#(and(X1,X2)) -> mark#(X1)
    mark#(and(X1,X2)) -> a__and#(mark(X1),X2)
    mark#(if(X1,X2,X3)) -> mark#(X1)
    mark#(if(X1,X2,X3)) -> a__if#(mark(X1),X2,X3)
    mark#(add(X1,X2)) -> mark#(X1)
    mark#(add(X1,X2)) -> a__add#(mark(X1),X2)
    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)) -> a__from#(X)
   TRS:
    a__and(true(),X) -> mark(X)
    a__and(false(),Y) -> false()
    a__if(true(),X,Y) -> mark(X)
    a__if(false(),X,Y) -> mark(Y)
    a__add(0(),X) -> mark(X)
    a__add(s(X),Y) -> s(add(X,Y))
    a__first(0(),X) -> nil()
    a__first(s(X),cons(Y,Z)) -> cons(Y,first(X,Z))
    a__from(X) -> cons(X,from(s(X)))
    mark(and(X1,X2)) -> a__and(mark(X1),X2)
    mark(if(X1,X2,X3)) -> a__if(mark(X1),X2,X3)
    mark(add(X1,X2)) -> a__add(mark(X1),X2)
    mark(first(X1,X2)) -> a__first(mark(X1),mark(X2))
    mark(from(X)) -> a__from(X)
    mark(true()) -> true()
    mark(false()) -> false()
    mark(0()) -> 0()
    mark(s(X)) -> s(X)
    mark(nil()) -> nil()
    mark(cons(X1,X2)) -> cons(X1,X2)
    a__and(X1,X2) -> and(X1,X2)
    a__if(X1,X2,X3) -> if(X1,X2,X3)
    a__add(X1,X2) -> add(X1,X2)
    a__first(X1,X2) -> first(X1,X2)
    a__from(X) -> from(X)
   graph:
    a__add#(0(),X) -> mark#(X) -> mark#(from(X)) -> a__from#(X)
    a__add#(0(),X) -> mark#(X) ->
    mark#(first(X1,X2)) -> a__first#(mark(X1),mark(X2))
    a__add#(0(),X) -> mark#(X) -> mark#(first(X1,X2)) -> mark#(X1)
    a__add#(0(),X) -> mark#(X) -> mark#(first(X1,X2)) -> mark#(X2)
    a__add#(0(),X) -> mark#(X) ->
    mark#(add(X1,X2)) -> a__add#(mark(X1),X2)
    a__add#(0(),X) -> mark#(X) -> mark#(add(X1,X2)) -> mark#(X1)
    a__add#(0(),X) -> mark#(X) ->
    mark#(if(X1,X2,X3)) -> a__if#(mark(X1),X2,X3)
    a__add#(0(),X) -> mark#(X) -> mark#(if(X1,X2,X3)) -> mark#(X1)
    a__add#(0(),X) -> mark#(X) ->
    mark#(and(X1,X2)) -> a__and#(mark(X1),X2)
    a__add#(0(),X) -> mark#(X) -> mark#(and(X1,X2)) -> mark#(X1)
    a__if#(false(),X,Y) -> mark#(Y) -> mark#(from(X)) -> a__from#(X)
    a__if#(false(),X,Y) -> mark#(Y) ->
    mark#(first(X1,X2)) -> a__first#(mark(X1),mark(X2))
    a__if#(false(),X,Y) -> mark#(Y) ->
    mark#(first(X1,X2)) -> mark#(X1)
    a__if#(false(),X,Y) -> mark#(Y) ->
    mark#(first(X1,X2)) -> mark#(X2)
    a__if#(false(),X,Y) -> mark#(Y) ->
    mark#(add(X1,X2)) -> a__add#(mark(X1),X2)
    a__if#(false(),X,Y) -> mark#(Y) ->
    mark#(add(X1,X2)) -> mark#(X1)
    a__if#(false(),X,Y) -> mark#(Y) ->
    mark#(if(X1,X2,X3)) -> a__if#(mark(X1),X2,X3)
    a__if#(false(),X,Y) -> mark#(Y) ->
    mark#(if(X1,X2,X3)) -> mark#(X1)
    a__if#(false(),X,Y) -> mark#(Y) ->
    mark#(and(X1,X2)) -> a__and#(mark(X1),X2)
    a__if#(false(),X,Y) -> mark#(Y) -> mark#(and(X1,X2)) -> mark#(X1)
    a__if#(true(),X,Y) -> mark#(X) -> mark#(from(X)) -> a__from#(X)
    a__if#(true(),X,Y) -> mark#(X) ->
    mark#(first(X1,X2)) -> a__first#(mark(X1),mark(X2))
    a__if#(true(),X,Y) -> mark#(X) ->
    mark#(first(X1,X2)) -> mark#(X1)
    a__if#(true(),X,Y) -> mark#(X) ->
    mark#(first(X1,X2)) -> mark#(X2)
    a__if#(true(),X,Y) -> mark#(X) ->
    mark#(add(X1,X2)) -> a__add#(mark(X1),X2)
    a__if#(true(),X,Y) -> mark#(X) -> mark#(add(X1,X2)) -> mark#(X1)
    a__if#(true(),X,Y) -> mark#(X) ->
    mark#(if(X1,X2,X3)) -> a__if#(mark(X1),X2,X3)
    a__if#(true(),X,Y) -> mark#(X) ->
    mark#(if(X1,X2,X3)) -> mark#(X1)
    a__if#(true(),X,Y) -> mark#(X) ->
    mark#(and(X1,X2)) -> a__and#(mark(X1),X2)
    a__if#(true(),X,Y) -> mark#(X) ->
    mark#(and(X1,X2)) -> mark#(X1)
    mark#(if(X1,X2,X3)) -> a__if#(mark(X1),X2,X3) ->
    a__if#(false(),X,Y) -> mark#(Y)
    mark#(if(X1,X2,X3)) -> a__if#(mark(X1),X2,X3) ->
    a__if#(true(),X,Y) -> mark#(X)
    mark#(if(X1,X2,X3)) -> mark#(X1) ->
    mark#(from(X)) -> a__from#(X)
    mark#(if(X1,X2,X3)) -> mark#(X1) ->
    mark#(first(X1,X2)) -> a__first#(mark(X1),mark(X2))
    mark#(if(X1,X2,X3)) -> mark#(X1) ->
    mark#(first(X1,X2)) -> mark#(X1)
    mark#(if(X1,X2,X3)) -> mark#(X1) ->
    mark#(first(X1,X2)) -> mark#(X2)
    mark#(if(X1,X2,X3)) -> mark#(X1) ->
    mark#(add(X1,X2)) -> a__add#(mark(X1),X2)
    mark#(if(X1,X2,X3)) -> mark#(X1) ->
    mark#(add(X1,X2)) -> mark#(X1)
    mark#(if(X1,X2,X3)) -> mark#(X1) ->
    mark#(if(X1,X2,X3)) -> a__if#(mark(X1),X2,X3)
    mark#(if(X1,X2,X3)) -> mark#(X1) ->
    mark#(if(X1,X2,X3)) -> mark#(X1)
    mark#(if(X1,X2,X3)) -> mark#(X1) ->
    mark#(and(X1,X2)) -> a__and#(mark(X1),X2)
    mark#(if(X1,X2,X3)) -> mark#(X1) ->
    mark#(and(X1,X2)) -> mark#(X1)
    mark#(and(X1,X2)) -> mark#(X1) -> mark#(from(X)) -> a__from#(X)
    mark#(and(X1,X2)) -> mark#(X1) ->
    mark#(first(X1,X2)) -> a__first#(mark(X1),mark(X2))
    mark#(and(X1,X2)) -> mark#(X1) ->
    mark#(first(X1,X2)) -> mark#(X1)
    mark#(and(X1,X2)) -> mark#(X1) ->
    mark#(first(X1,X2)) -> mark#(X2)
    mark#(and(X1,X2)) -> mark#(X1) ->
    mark#(add(X1,X2)) -> a__add#(mark(X1),X2)
    mark#(and(X1,X2)) -> mark#(X1) -> mark#(add(X1,X2)) -> mark#(X1)
    mark#(and(X1,X2)) -> mark#(X1) ->
    mark#(if(X1,X2,X3)) -> a__if#(mark(X1),X2,X3)
    mark#(and(X1,X2)) -> mark#(X1) ->
    mark#(if(X1,X2,X3)) -> mark#(X1)
    mark#(and(X1,X2)) -> mark#(X1) ->
    mark#(and(X1,X2)) -> a__and#(mark(X1),X2)
    mark#(and(X1,X2)) -> mark#(X1) ->
    mark#(and(X1,X2)) -> mark#(X1)
    mark#(and(X1,X2)) -> a__and#(mark(X1),X2) ->
    a__and#(true(),X) -> mark#(X)
    mark#(first(X1,X2)) -> mark#(X2) ->
    mark#(from(X)) -> a__from#(X)
    mark#(first(X1,X2)) -> mark#(X2) ->
    mark#(first(X1,X2)) -> a__first#(mark(X1),mark(X2))
    mark#(first(X1,X2)) -> mark#(X2) ->
    mark#(first(X1,X2)) -> mark#(X1)
    mark#(first(X1,X2)) -> mark#(X2) ->
    mark#(first(X1,X2)) -> mark#(X2)
    mark#(first(X1,X2)) -> mark#(X2) ->
    mark#(add(X1,X2)) -> a__add#(mark(X1),X2)
    mark#(first(X1,X2)) -> mark#(X2) ->
    mark#(add(X1,X2)) -> mark#(X1)
    mark#(first(X1,X2)) -> mark#(X2) ->
    mark#(if(X1,X2,X3)) -> a__if#(mark(X1),X2,X3)
    mark#(first(X1,X2)) -> mark#(X2) ->
    mark#(if(X1,X2,X3)) -> mark#(X1)
    mark#(first(X1,X2)) -> mark#(X2) ->
    mark#(and(X1,X2)) -> a__and#(mark(X1),X2)
    mark#(first(X1,X2)) -> mark#(X2) ->
    mark#(and(X1,X2)) -> mark#(X1)
    mark#(first(X1,X2)) -> mark#(X1) ->
    mark#(from(X)) -> a__from#(X)
    mark#(first(X1,X2)) -> mark#(X1) ->
    mark#(first(X1,X2)) -> a__first#(mark(X1),mark(X2))
    mark#(first(X1,X2)) -> mark#(X1) ->
    mark#(first(X1,X2)) -> mark#(X1)
    mark#(first(X1,X2)) -> mark#(X1) ->
    mark#(first(X1,X2)) -> mark#(X2)
    mark#(first(X1,X2)) -> mark#(X1) ->
    mark#(add(X1,X2)) -> a__add#(mark(X1),X2)
    mark#(first(X1,X2)) -> mark#(X1) ->
    mark#(add(X1,X2)) -> mark#(X1)
    mark#(first(X1,X2)) -> mark#(X1) ->
    mark#(if(X1,X2,X3)) -> a__if#(mark(X1),X2,X3)
    mark#(first(X1,X2)) -> mark#(X1) ->
    mark#(if(X1,X2,X3)) -> mark#(X1)
    mark#(first(X1,X2)) -> mark#(X1) ->
    mark#(and(X1,X2)) -> a__and#(mark(X1),X2)
    mark#(first(X1,X2)) -> mark#(X1) ->
    mark#(and(X1,X2)) -> mark#(X1)
    mark#(add(X1,X2)) -> a__add#(mark(X1),X2) ->
    a__add#(0(),X) -> mark#(X)
    mark#(add(X1,X2)) -> mark#(X1) -> mark#(from(X)) -> a__from#(X)
    mark#(add(X1,X2)) -> mark#(X1) ->
    mark#(first(X1,X2)) -> a__first#(mark(X1),mark(X2))
    mark#(add(X1,X2)) -> mark#(X1) ->
    mark#(first(X1,X2)) -> mark#(X1)
    mark#(add(X1,X2)) -> mark#(X1) ->
    mark#(first(X1,X2)) -> mark#(X2)
    mark#(add(X1,X2)) -> mark#(X1) ->
    mark#(add(X1,X2)) -> a__add#(mark(X1),X2)
    mark#(add(X1,X2)) -> mark#(X1) -> mark#(add(X1,X2)) -> mark#(X1)
    mark#(add(X1,X2)) -> mark#(X1) ->
    mark#(if(X1,X2,X3)) -> a__if#(mark(X1),X2,X3)
    mark#(add(X1,X2)) -> mark#(X1) ->
    mark#(if(X1,X2,X3)) -> mark#(X1)
    mark#(add(X1,X2)) -> mark#(X1) ->
    mark#(and(X1,X2)) -> a__and#(mark(X1),X2)
    mark#(add(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> mark#(X1)
    a__and#(true(),X) -> mark#(X) -> mark#(from(X)) -> a__from#(X)
    a__and#(true(),X) -> mark#(X) ->
    mark#(first(X1,X2)) -> a__first#(mark(X1),mark(X2))
    a__and#(true(),X) -> mark#(X) -> mark#(first(X1,X2)) -> mark#(X1)
    a__and#(true(),X) -> mark#(X) -> mark#(first(X1,X2)) -> mark#(X2)
    a__and#(true(),X) -> mark#(X) ->
    mark#(add(X1,X2)) -> a__add#(mark(X1),X2)
    a__and#(true(),X) -> mark#(X) -> mark#(add(X1,X2)) -> mark#(X1)
    a__and#(true(),X) -> mark#(X) ->
    mark#(if(X1,X2,X3)) -> a__if#(mark(X1),X2,X3)
    a__and#(true(),X) -> mark#(X) -> mark#(if(X1,X2,X3)) -> mark#(X1)
    a__and#(true(),X) -> mark#(X) ->
    mark#(and(X1,X2)) -> a__and#(mark(X1),X2)
    a__and#(true(),X) -> mark#(X) -> mark#(and(X1,X2)) -> mark#(X1)
   SCC Processor:
    #sccs: 1
    #rules: 12
    #arcs: 94/196
    DPs:
     a__add#(0(),X) -> mark#(X)
     mark#(and(X1,X2)) -> mark#(X1)
     mark#(and(X1,X2)) -> a__and#(mark(X1),X2)
     a__and#(true(),X) -> mark#(X)
     mark#(if(X1,X2,X3)) -> mark#(X1)
     mark#(if(X1,X2,X3)) -> a__if#(mark(X1),X2,X3)
     a__if#(true(),X,Y) -> mark#(X)
     mark#(add(X1,X2)) -> mark#(X1)
     mark#(add(X1,X2)) -> a__add#(mark(X1),X2)
     mark#(first(X1,X2)) -> mark#(X2)
     mark#(first(X1,X2)) -> mark#(X1)
     a__if#(false(),X,Y) -> mark#(Y)
    TRS:
     a__and(true(),X) -> mark(X)
     a__and(false(),Y) -> false()
     a__if(true(),X,Y) -> mark(X)
     a__if(false(),X,Y) -> mark(Y)
     a__add(0(),X) -> mark(X)
     a__add(s(X),Y) -> s(add(X,Y))
     a__first(0(),X) -> nil()
     a__first(s(X),cons(Y,Z)) -> cons(Y,first(X,Z))
     a__from(X) -> cons(X,from(s(X)))
     mark(and(X1,X2)) -> a__and(mark(X1),X2)
     mark(if(X1,X2,X3)) -> a__if(mark(X1),X2,X3)
     mark(add(X1,X2)) -> a__add(mark(X1),X2)
     mark(first(X1,X2)) -> a__first(mark(X1),mark(X2))
     mark(from(X)) -> a__from(X)
     mark(true()) -> true()
     mark(false()) -> false()
     mark(0()) -> 0()
     mark(s(X)) -> s(X)
     mark(nil()) -> nil()
     mark(cons(X1,X2)) -> cons(X1,X2)
     a__and(X1,X2) -> and(X1,X2)
     a__if(X1,X2,X3) -> if(X1,X2,X3)
     a__add(X1,X2) -> add(X1,X2)
     a__first(X1,X2) -> first(X1,X2)
     a__from(X) -> from(X)
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [a__add#](x0, x1) = x0 + x1 + 1/2,
      
      [a__if#](x0, x1, x2) = x1 + 2x2 + 1,
      
      [mark#](x0) = x0,
      
      [a__and#](x0, x1) = 1/2x0 + x1,
      
      [if](x0, x1, x2) = x0 + x1 + 7/2x2 + 3/2,
      
      [and](x0, x1) = x0 + x1 + 1/2,
      
      [from](x0) = x0 + 1/2,
      
      [a__from](x0) = 3/2x0 + 1,
      
      [first](x0, x1) = 2x0 + 3/2x1 + 1,
      
      [cons](x0, x1) = 0,
      
      [nil] = 7/2,
      
      [a__first](x0, x1) = 2x0 + 3/2x1 + 1,
      
      [add](x0, x1) = 2x0 + 2x1 + 1,
      
      [s](x0) = 0,
      
      [a__add](x0, x1) = 2x0 + 5/2x1 + 2,
      
      [0] = 2,
      
      [a__if](x0, x1, x2) = x0 + 2x1 + 7/2x2 + 3/2,
      
      [false] = 3,
      
      [mark](x0) = 2x0,
      
      [a__and](x0, x1) = x0 + 2x1 + 1,
      
      [true] = 1
     orientation:
      a__add#(0(),X) = X + 5/2 >= X = mark#(X)
      
      mark#(and(X1,X2)) = X1 + X2 + 1/2 >= X1 = mark#(X1)
      
      mark#(and(X1,X2)) = X1 + X2 + 1/2 >= X1 + X2 = a__and#(mark(X1),X2)
      
      a__and#(true(),X) = X + 1/2 >= X = mark#(X)
      
      mark#(if(X1,X2,X3)) = X1 + X2 + 7/2X3 + 3/2 >= X1 = mark#(X1)
      
      mark#(if(X1,X2,X3)) = X1 + X2 + 7/2X3 + 3/2 >= X2 + 2X3 + 1 = a__if#(mark(X1),X2,X3)
      
      a__if#(true(),X,Y) = X + 2Y + 1 >= X = mark#(X)
      
      mark#(add(X1,X2)) = 2X1 + 2X2 + 1 >= X1 = mark#(X1)
      
      mark#(add(X1,X2)) = 2X1 + 2X2 + 1 >= 2X1 + X2 + 1/2 = a__add#(mark(X1),X2)
      
      mark#(first(X1,X2)) = 2X1 + 3/2X2 + 1 >= X2 = mark#(X2)
      
      mark#(first(X1,X2)) = 2X1 + 3/2X2 + 1 >= X1 = mark#(X1)
      
      a__if#(false(),X,Y) = X + 2Y + 1 >= Y = mark#(Y)
      
      a__and(true(),X) = 2X + 2 >= 2X = mark(X)
      
      a__and(false(),Y) = 2Y + 4 >= 3 = false()
      
      a__if(true(),X,Y) = 2X + 7/2Y + 5/2 >= 2X = mark(X)
      
      a__if(false(),X,Y) = 2X + 7/2Y + 9/2 >= 2Y = mark(Y)
      
      a__add(0(),X) = 5/2X + 6 >= 2X = mark(X)
      
      a__add(s(X),Y) = 5/2Y + 2 >= 0 = s(add(X,Y))
      
      a__first(0(),X) = 3/2X + 5 >= 7/2 = nil()
      
      a__first(s(X),cons(Y,Z)) = 1 >= 0 = cons(Y,first(X,Z))
      
      a__from(X) = 3/2X + 1 >= 0 = cons(X,from(s(X)))
      
      mark(and(X1,X2)) = 2X1 + 2X2 + 1 >= 2X1 + 2X2 + 1 = a__and(mark(X1),X2)
      
      mark(if(X1,X2,X3)) = 2X1 + 2X2 + 7X3 + 3 >= 2X1 + 2X2 + 7/2X3 + 3/2 = a__if(mark(X1),X2,X3)
      
      mark(add(X1,X2)) = 4X1 + 4X2 + 2 >= 4X1 + 5/2X2 + 2 = a__add(mark(X1),X2)
      
      mark(first(X1,X2)) = 4X1 + 3X2 + 2 >= 4X1 + 3X2 + 1 = a__first(mark(X1),mark(X2))
      
      mark(from(X)) = 2X + 1 >= 3/2X + 1 = a__from(X)
      
      mark(true()) = 2 >= 1 = true()
      
      mark(false()) = 6 >= 3 = false()
      
      mark(0()) = 4 >= 2 = 0()
      
      mark(s(X)) = 0 >= 0 = s(X)
      
      mark(nil()) = 7 >= 7/2 = nil()
      
      mark(cons(X1,X2)) = 0 >= 0 = cons(X1,X2)
      
      a__and(X1,X2) = X1 + 2X2 + 1 >= X1 + X2 + 1/2 = and(X1,X2)
      
      a__if(X1,X2,X3) = X1 + 2X2 + 7/2X3 + 3/2 >= X1 + X2 + 7/2X3 + 3/2 = if(X1,X2,X3)
      
      a__add(X1,X2) = 2X1 + 5/2X2 + 2 >= 2X1 + 2X2 + 1 = add(X1,X2)
      
      a__first(X1,X2) = 2X1 + 3/2X2 + 1 >= 2X1 + 3/2X2 + 1 = first(X1,X2)
      
      a__from(X) = 3/2X + 1 >= X + 1/2 = from(X)
     problem:
      DPs:
       
      TRS:
       a__and(true(),X) -> mark(X)
       a__and(false(),Y) -> false()
       a__if(true(),X,Y) -> mark(X)
       a__if(false(),X,Y) -> mark(Y)
       a__add(0(),X) -> mark(X)
       a__add(s(X),Y) -> s(add(X,Y))
       a__first(0(),X) -> nil()
       a__first(s(X),cons(Y,Z)) -> cons(Y,first(X,Z))
       a__from(X) -> cons(X,from(s(X)))
       mark(and(X1,X2)) -> a__and(mark(X1),X2)
       mark(if(X1,X2,X3)) -> a__if(mark(X1),X2,X3)
       mark(add(X1,X2)) -> a__add(mark(X1),X2)
       mark(first(X1,X2)) -> a__first(mark(X1),mark(X2))
       mark(from(X)) -> a__from(X)
       mark(true()) -> true()
       mark(false()) -> false()
       mark(0()) -> 0()
       mark(s(X)) -> s(X)
       mark(nil()) -> nil()
       mark(cons(X1,X2)) -> cons(X1,X2)
       a__and(X1,X2) -> and(X1,X2)
       a__if(X1,X2,X3) -> if(X1,X2,X3)
       a__add(X1,X2) -> add(X1,X2)
       a__first(X1,X2) -> first(X1,X2)
       a__from(X) -> from(X)
     Qed