NO

Problem:
 app(app(app(if(),true()),xs),ys) -> xs
 app(app(app(if(),false()),xs),ys) -> ys
 app(app(lt(),app(s(),x)),app(s(),y)) -> app(app(lt(),x),y)
 app(app(lt(),0()),app(s(),y)) -> true()
 app(app(lt(),y),0()) -> false()
 app(app(eq(),x),x) -> true()
 app(app(eq(),app(s(),x)),0()) -> false()
 app(app(eq(),0()),app(s(),x)) -> false()
 app(app(merge(),xs),nil()) -> xs
 app(app(merge(),nil()),ys) -> ys
 app(app(merge(),app(app(cons(),x),xs)),app(app(cons(),y),ys)) ->
 app(app(app(if(),app(app(lt(),x),y)),app(app(cons(),x),app(app(merge(),xs),app(app(cons(),y),ys)))),
     app(app(app(if(),app(app(eq(),x),y)),app(app(cons(),x),app(app(merge(),xs),ys))),
         app(app(cons(),y),app(app(merge(),app(app(cons(),x),xs)),ys))))
 app(app(map(),f),nil()) -> nil()
 app(app(map(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(f,x)),app(app(map(),f),xs))
 app(app(mult(),0()),x) -> 0()
 app(app(mult(),app(s(),x)),y) -> app(app(plus(),y),app(app(mult(),x),y))
 app(app(plus(),0()),x) -> 0()
 app(app(plus(),app(s(),x)),y) -> app(s(),app(app(plus(),x),y))
 list1() -> app(app(map(),app(mult(),app(s(),app(s(),0())))),hamming())
 list2() -> app(app(map(),app(mult(),app(s(),app(s(),app(s(),0()))))),hamming())
 list3() -> app(app(map(),app(mult(),app(s(),app(s(),app(s(),app(s(),app(s(),0()))))))),hamming())
 hamming() ->
 app(app(cons(),app(s(),0())),app(app(merge(),list1()),app(app(merge(),list2()),list3())))

Proof:
 Uncurry Processor:
  if3(true(),xs,ys) -> xs
  if3(false(),xs,ys) -> ys
  lt2(s1(x),s1(y)) -> lt2(x,y)
  lt2(0(),s1(y)) -> true()
  lt2(y,0()) -> false()
  eq2(x,x) -> true()
  eq2(s1(x),0()) -> false()
  eq2(0(),s1(x)) -> false()
  merge2(xs,nil()) -> xs
  merge2(nil(),ys) -> ys
  merge2(cons2(x,xs),cons2(y,ys)) ->
  if3(lt2(x,y),cons2(x,merge2(xs,cons2(y,ys))),if3(eq2(x,y),cons2(x,merge2(xs,ys)),
                                                   cons2(y,merge2(cons2(x,xs),ys))))
  map2(f,nil()) -> nil()
  map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
  mult2(0(),x) -> 0()
  mult2(s1(x),y) -> plus2(y,mult2(x,y))
  plus2(0(),x) -> 0()
  plus2(s1(x),y) -> s1(plus2(x,y))
  list1() -> map2(mult1(s1(s1(0()))),hamming())
  list2() -> map2(mult1(s1(s1(s1(0())))),hamming())
  list3() -> map2(mult1(s1(s1(s1(s1(s1(0())))))),hamming())
  hamming() -> cons2(s1(0()),merge2(list1(),merge2(list2(),list3())))
  app(if2(x6,x5),x7) -> if3(x6,x5,x7)
  app(if1(x6),x7) -> if2(x6,x7)
  app(if(),x7) -> if1(x7)
  app(lt1(x6),x7) -> lt2(x6,x7)
  app(lt(),x7) -> lt1(x7)
  app(s(),x7) -> s1(x7)
  app(eq1(x6),x7) -> eq2(x6,x7)
  app(eq(),x7) -> eq1(x7)
  app(merge1(x6),x7) -> merge2(x6,x7)
  app(merge(),x7) -> merge1(x7)
  app(cons1(x6),x7) -> cons2(x6,x7)
  app(cons(),x7) -> cons1(x7)
  app(map1(x6),x7) -> map2(x6,x7)
  app(map(),x7) -> map1(x7)
  app(mult1(x6),x7) -> mult2(x6,x7)
  app(mult(),x7) -> mult1(x7)
  app(plus1(x6),x7) -> plus2(x6,x7)
  app(plus(),x7) -> plus1(x7)
  Unfolding Processor:
   loop length: 2
   terms:
    list1()
    map2(mult1(s1(s1(0()))),hamming())
   context: map2(mult1(s1(s1(0()))),cons2(s1(0()),merge2([],merge2(list2(),list3()))))
   substitution:
    
   Qed