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:
     dimension: 1
     interpretation:
      [a__add#](x0, x1) = x0 + x1 + 1,
      
      [a__if#](x0, x1, x2) = x0 + x1 + x2 + 1,
      
      [mark#](x0) = x0 + 1,
      
      [a__and#](x0, x1) = x0 + x1,
      
      [if](x0, x1, x2) = x0 + x1 + x2,
      
      [and](x0, x1) = x0 + x1 + 1,
      
      [from](x0) = 1,
      
      [a__from](x0) = 1,
      
      [first](x0, x1) = x0 + x1,
      
      [cons](x0, x1) = 1,
      
      [nil] = 1,
      
      [a__first](x0, x1) = x0 + x1,
      
      [add](x0, x1) = x0 + x1,
      
      [s](x0) = 0,
      
      [a__add](x0, x1) = x0 + x1,
      
      [0] = 1,
      
      [a__if](x0, x1, x2) = x0 + x1 + x2,
      
      [false] = 0,
      
      [mark](x0) = x0,
      
      [a__and](x0, x1) = x0 + x1 + 1,
      
      [true] = 1
     orientation:
      a__add#(0(),X) = X + 2 >= X + 1 = mark#(X)
      
      mark#(and(X1,X2)) = X1 + X2 + 2 >= X1 + 1 = mark#(X1)
      
      mark#(and(X1,X2)) = X1 + X2 + 2 >= X1 + X2 = a__and#(mark(X1),X2)
      
      a__and#(true(),X) = X + 1 >= X + 1 = mark#(X)
      
      mark#(if(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + 1 = mark#(X1)
      
      mark#(if(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = a__if#(mark(X1),X2,X3)
      
      a__if#(true(),X,Y) = X + Y + 2 >= X + 1 = mark#(X)
      
      mark#(add(X1,X2)) = X1 + X2 + 1 >= X1 + 1 = mark#(X1)
      
      mark#(add(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = a__add#(mark(X1),X2)
      
      mark#(first(X1,X2)) = X1 + X2 + 1 >= X2 + 1 = mark#(X2)
      
      mark#(first(X1,X2)) = X1 + X2 + 1 >= X1 + 1 = mark#(X1)
      
      a__if#(false(),X,Y) = X + Y + 1 >= Y + 1 = mark#(Y)
      
      a__and(true(),X) = X + 2 >= X = mark(X)
      
      a__and(false(),Y) = Y + 1 >= 0 = false()
      
      a__if(true(),X,Y) = X + Y + 1 >= X = mark(X)
      
      a__if(false(),X,Y) = X + Y >= Y = mark(Y)
      
      a__add(0(),X) = X + 1 >= X = mark(X)
      
      a__add(s(X),Y) = Y >= 0 = s(add(X,Y))
      
      a__first(0(),X) = X + 1 >= 1 = nil()
      
      a__first(s(X),cons(Y,Z)) = 1 >= 1 = cons(Y,first(X,Z))
      
      a__from(X) = 1 >= 1 = cons(X,from(s(X)))
      
      mark(and(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = a__and(mark(X1),X2)
      
      mark(if(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__if(mark(X1),X2,X3)
      
      mark(add(X1,X2)) = X1 + X2 >= X1 + X2 = a__add(mark(X1),X2)
      
      mark(first(X1,X2)) = X1 + X2 >= X1 + X2 = a__first(mark(X1),mark(X2))
      
      mark(from(X)) = 1 >= 1 = a__from(X)
      
      mark(true()) = 1 >= 1 = true()
      
      mark(false()) = 0 >= 0 = false()
      
      mark(0()) = 1 >= 1 = 0()
      
      mark(s(X)) = 0 >= 0 = s(X)
      
      mark(nil()) = 1 >= 1 = nil()
      
      mark(cons(X1,X2)) = 1 >= 1 = cons(X1,X2)
      
      a__and(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 1 = and(X1,X2)
      
      a__if(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = if(X1,X2,X3)
      
      a__add(X1,X2) = X1 + X2 >= X1 + X2 = add(X1,X2)
      
      a__first(X1,X2) = X1 + X2 >= X1 + X2 = first(X1,X2)
      
      a__from(X) = 1 >= 1 = from(X)
     problem:
      DPs:
       a__and#(true(),X) -> mark#(X)
       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)
       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:
      dimension: 1
      interpretation:
       [a__add#](x0, x1) = 0,
       
       [a__if#](x0, x1, x2) = 0,
       
       [mark#](x0) = 0,
       
       [a__and#](x0, x1) = x0 + 1,
       
       [if](x0, x1, x2) = 1,
       
       [and](x0, x1) = 1,
       
       [from](x0) = 1,
       
       [a__from](x0) = 1,
       
       [first](x0, x1) = 1,
       
       [cons](x0, x1) = 1,
       
       [nil] = 1,
       
       [a__first](x0, x1) = 1,
       
       [add](x0, x1) = 1,
       
       [s](x0) = 1,
       
       [a__add](x0, x1) = 1,
       
       [0] = 1,
       
       [a__if](x0, x1, x2) = 1,
       
       [false] = 1,
       
       [mark](x0) = 1,
       
       [a__and](x0, x1) = 1,
       
       [true] = 1
      orientation:
       a__and#(true(),X) = 2 >= 0 = mark#(X)
       
       mark#(if(X1,X2,X3)) = 0 >= 0 = mark#(X1)
       
       mark#(if(X1,X2,X3)) = 0 >= 0 = a__if#(mark(X1),X2,X3)
       
       mark#(add(X1,X2)) = 0 >= 0 = mark#(X1)
       
       mark#(add(X1,X2)) = 0 >= 0 = a__add#(mark(X1),X2)
       
       mark#(first(X1,X2)) = 0 >= 0 = mark#(X2)
       
       mark#(first(X1,X2)) = 0 >= 0 = mark#(X1)
       
       a__if#(false(),X,Y) = 0 >= 0 = mark#(Y)
       
       a__and(true(),X) = 1 >= 1 = mark(X)
       
       a__and(false(),Y) = 1 >= 1 = false()
       
       a__if(true(),X,Y) = 1 >= 1 = mark(X)
       
       a__if(false(),X,Y) = 1 >= 1 = mark(Y)
       
       a__add(0(),X) = 1 >= 1 = mark(X)
       
       a__add(s(X),Y) = 1 >= 1 = s(add(X,Y))
       
       a__first(0(),X) = 1 >= 1 = nil()
       
       a__first(s(X),cons(Y,Z)) = 1 >= 1 = cons(Y,first(X,Z))
       
       a__from(X) = 1 >= 1 = cons(X,from(s(X)))
       
       mark(and(X1,X2)) = 1 >= 1 = a__and(mark(X1),X2)
       
       mark(if(X1,X2,X3)) = 1 >= 1 = a__if(mark(X1),X2,X3)
       
       mark(add(X1,X2)) = 1 >= 1 = a__add(mark(X1),X2)
       
       mark(first(X1,X2)) = 1 >= 1 = a__first(mark(X1),mark(X2))
       
       mark(from(X)) = 1 >= 1 = a__from(X)
       
       mark(true()) = 1 >= 1 = true()
       
       mark(false()) = 1 >= 1 = false()
       
       mark(0()) = 1 >= 1 = 0()
       
       mark(s(X)) = 1 >= 1 = s(X)
       
       mark(nil()) = 1 >= 1 = nil()
       
       mark(cons(X1,X2)) = 1 >= 1 = cons(X1,X2)
       
       a__and(X1,X2) = 1 >= 1 = and(X1,X2)
       
       a__if(X1,X2,X3) = 1 >= 1 = if(X1,X2,X3)
       
       a__add(X1,X2) = 1 >= 1 = add(X1,X2)
       
       a__first(X1,X2) = 1 >= 1 = first(X1,X2)
       
       a__from(X) = 1 >= 1 = from(X)
      problem:
       DPs:
        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)
        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:
       dimension: 1
       interpretation:
        [a__add#](x0, x1) = 0,
        
        [a__if#](x0, x1, x2) = x0 + x2 + 1,
        
        [mark#](x0) = x0 + 1,
        
        [if](x0, x1, x2) = x0 + x1 + x2 + 1,
        
        [and](x0, x1) = x1,
        
        [from](x0) = 0,
        
        [a__from](x0) = 0,
        
        [first](x0, x1) = x0 + x1,
        
        [cons](x0, x1) = 0,
        
        [nil] = 1,
        
        [a__first](x0, x1) = x0 + x1,
        
        [add](x0, x1) = x0 + x1,
        
        [s](x0) = 0,
        
        [a__add](x0, x1) = x0 + x1,
        
        [0] = 1,
        
        [a__if](x0, x1, x2) = x0 + x1 + x2 + 1,
        
        [false] = 0,
        
        [mark](x0) = x0,
        
        [a__and](x0, x1) = x1,
        
        [true] = 1
       orientation:
        mark#(if(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X1 + 1 = mark#(X1)
        
        mark#(if(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X1 + X3 + 1 = a__if#(mark(X1),X2,X3)
        
        mark#(add(X1,X2)) = X1 + X2 + 1 >= X1 + 1 = mark#(X1)
        
        mark#(add(X1,X2)) = X1 + X2 + 1 >= 0 = a__add#(mark(X1),X2)
        
        mark#(first(X1,X2)) = X1 + X2 + 1 >= X2 + 1 = mark#(X2)
        
        mark#(first(X1,X2)) = X1 + X2 + 1 >= X1 + 1 = mark#(X1)
        
        a__if#(false(),X,Y) = Y + 1 >= Y + 1 = mark#(Y)
        
        a__and(true(),X) = X >= X = mark(X)
        
        a__and(false(),Y) = Y >= 0 = false()
        
        a__if(true(),X,Y) = X + Y + 2 >= X = mark(X)
        
        a__if(false(),X,Y) = X + Y + 1 >= Y = mark(Y)
        
        a__add(0(),X) = X + 1 >= X = mark(X)
        
        a__add(s(X),Y) = Y >= 0 = s(add(X,Y))
        
        a__first(0(),X) = X + 1 >= 1 = nil()
        
        a__first(s(X),cons(Y,Z)) = 0 >= 0 = cons(Y,first(X,Z))
        
        a__from(X) = 0 >= 0 = cons(X,from(s(X)))
        
        mark(and(X1,X2)) = X2 >= X2 = a__and(mark(X1),X2)
        
        mark(if(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = a__if(mark(X1),X2,X3)
        
        mark(add(X1,X2)) = X1 + X2 >= X1 + X2 = a__add(mark(X1),X2)
        
        mark(first(X1,X2)) = X1 + X2 >= X1 + X2 = a__first(mark(X1),mark(X2))
        
        mark(from(X)) = 0 >= 0 = a__from(X)
        
        mark(true()) = 1 >= 1 = true()
        
        mark(false()) = 0 >= 0 = false()
        
        mark(0()) = 1 >= 1 = 0()
        
        mark(s(X)) = 0 >= 0 = s(X)
        
        mark(nil()) = 1 >= 1 = nil()
        
        mark(cons(X1,X2)) = 0 >= 0 = cons(X1,X2)
        
        a__and(X1,X2) = X2 >= X2 = and(X1,X2)
        
        a__if(X1,X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = if(X1,X2,X3)
        
        a__add(X1,X2) = X1 + X2 >= X1 + X2 = add(X1,X2)
        
        a__first(X1,X2) = X1 + X2 >= X1 + X2 = first(X1,X2)
        
        a__from(X) = 0 >= 0 = from(X)
       problem:
        DPs:
         mark#(add(X1,X2)) -> mark#(X1)
         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:
        dimension: 1
        interpretation:
         [a__if#](x0, x1, x2) = x0 + x2 + 1,
         
         [mark#](x0) = x0 + 1,
         
         [if](x0, x1, x2) = x1 + x2,
         
         [and](x0, x1) = x1 + 1,
         
         [from](x0) = 0,
         
         [a__from](x0) = 0,
         
         [first](x0, x1) = x0 + x1 + 1,
         
         [cons](x0, x1) = 0,
         
         [nil] = 0,
         
         [a__first](x0, x1) = x0 + x1 + 1,
         
         [add](x0, x1) = x0 + x1 + 1,
         
         [s](x0) = 1,
         
         [a__add](x0, x1) = x0 + x1 + 1,
         
         [0] = 0,
         
         [a__if](x0, x1, x2) = x1 + x2,
         
         [false] = 1,
         
         [mark](x0) = x0,
         
         [a__and](x0, x1) = x1 + 1,
         
         [true] = 1
        orientation:
         mark#(add(X1,X2)) = X1 + X2 + 2 >= X1 + 1 = mark#(X1)
         
         mark#(first(X1,X2)) = X1 + X2 + 2 >= X2 + 1 = mark#(X2)
         
         mark#(first(X1,X2)) = X1 + X2 + 2 >= X1 + 1 = mark#(X1)
         
         a__if#(false(),X,Y) = Y + 2 >= Y + 1 = mark#(Y)
         
         a__and(true(),X) = X + 1 >= X = mark(X)
         
         a__and(false(),Y) = Y + 1 >= 1 = false()
         
         a__if(true(),X,Y) = X + Y >= X = mark(X)
         
         a__if(false(),X,Y) = X + Y >= Y = mark(Y)
         
         a__add(0(),X) = X + 1 >= X = mark(X)
         
         a__add(s(X),Y) = Y + 2 >= 1 = s(add(X,Y))
         
         a__first(0(),X) = X + 1 >= 0 = nil()
         
         a__first(s(X),cons(Y,Z)) = 2 >= 0 = cons(Y,first(X,Z))
         
         a__from(X) = 0 >= 0 = cons(X,from(s(X)))
         
         mark(and(X1,X2)) = X2 + 1 >= X2 + 1 = a__and(mark(X1),X2)
         
         mark(if(X1,X2,X3)) = X2 + X3 >= X2 + X3 = a__if(mark(X1),X2,X3)
         
         mark(add(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = a__add(mark(X1),X2)
         
         mark(first(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = a__first(mark(X1),mark(X2))
         
         mark(from(X)) = 0 >= 0 = a__from(X)
         
         mark(true()) = 1 >= 1 = true()
         
         mark(false()) = 1 >= 1 = false()
         
         mark(0()) = 0 >= 0 = 0()
         
         mark(s(X)) = 1 >= 1 = s(X)
         
         mark(nil()) = 0 >= 0 = nil()
         
         mark(cons(X1,X2)) = 0 >= 0 = cons(X1,X2)
         
         a__and(X1,X2) = X2 + 1 >= X2 + 1 = and(X1,X2)
         
         a__if(X1,X2,X3) = X2 + X3 >= X2 + X3 = if(X1,X2,X3)
         
         a__add(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 1 = add(X1,X2)
         
         a__first(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 1 = first(X1,X2)
         
         a__from(X) = 0 >= 0 = 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