YES

Problem:
 app(id(),x) -> x
 app(add(),0()) -> id()
 app(app(add(),app(s(),x)),y) -> app(s(),app(app(add(),x),y))
 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))

Proof:
 Uncurry Processor:
  id1(x) -> x
  add2(0(),x6) -> id1(x6)
  add1(0()) -> id()
  add2(s1(x),y) -> s1(add2(x,y))
  map2(f,nil()) -> nil()
  map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
  app(id(),x5) -> id1(x5)
  app(add1(x4),x5) -> add2(x4,x5)
  app(add(),x5) -> add1(x5)
  app(s(),x5) -> s1(x5)
  app(map1(x4),x5) -> map2(x4,x5)
  app(map(),x5) -> map1(x5)
  app(cons1(x4),x5) -> cons2(x4,x5)
  app(cons(),x5) -> cons1(x5)
  DP Processor:
   DPs:
    add{2,#}(0(),x6) -> id{1,#}(x6)
    add{2,#}(s1(x),y) -> add{2,#}(x,y)
    map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
    map{2,#}(f,cons2(x,xs)) -> app#(f,x)
    app#(id(),x5) -> id{1,#}(x5)
    app#(add1(x4),x5) -> add{2,#}(x4,x5)
    app#(add(),x5) -> add{1,#}(x5)
    app#(map1(x4),x5) -> map{2,#}(x4,x5)
   TRS:
    id1(x) -> x
    add2(0(),x6) -> id1(x6)
    add1(0()) -> id()
    add2(s1(x),y) -> s1(add2(x,y))
    map2(f,nil()) -> nil()
    map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
    app(id(),x5) -> id1(x5)
    app(add1(x4),x5) -> add2(x4,x5)
    app(add(),x5) -> add1(x5)
    app(s(),x5) -> s1(x5)
    app(map1(x4),x5) -> map2(x4,x5)
    app(map(),x5) -> map1(x5)
    app(cons1(x4),x5) -> cons2(x4,x5)
    app(cons(),x5) -> cons1(x5)
   TDG Processor:
    DPs:
     add{2,#}(0(),x6) -> id{1,#}(x6)
     add{2,#}(s1(x),y) -> add{2,#}(x,y)
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x)
     app#(id(),x5) -> id{1,#}(x5)
     app#(add1(x4),x5) -> add{2,#}(x4,x5)
     app#(add(),x5) -> add{1,#}(x5)
     app#(map1(x4),x5) -> map{2,#}(x4,x5)
    TRS:
     id1(x) -> x
     add2(0(),x6) -> id1(x6)
     add1(0()) -> id()
     add2(s1(x),y) -> s1(add2(x,y))
     map2(f,nil()) -> nil()
     map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
     app(id(),x5) -> id1(x5)
     app(add1(x4),x5) -> add2(x4,x5)
     app(add(),x5) -> add1(x5)
     app(s(),x5) -> s1(x5)
     app(map1(x4),x5) -> map2(x4,x5)
     app(map(),x5) -> map1(x5)
     app(cons1(x4),x5) -> cons2(x4,x5)
     app(cons(),x5) -> cons1(x5)
    graph:
     app#(map1(x4),x5) -> map{2,#}(x4,x5) ->
     map{2,#}(f,cons2(x,xs)) -> app#(f,x)
     app#(map1(x4),x5) -> map{2,#}(x4,x5) ->
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
     app#(add1(x4),x5) -> add{2,#}(x4,x5) ->
     add{2,#}(s1(x),y) -> add{2,#}(x,y)
     app#(add1(x4),x5) -> add{2,#}(x4,x5) ->
     add{2,#}(0(),x6) -> id{1,#}(x6)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(map1(x4),x5) -> map{2,#}(x4,x5)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(add(),x5) -> add{1,#}(x5)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(add1(x4),x5) -> add{2,#}(x4,x5)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(id(),x5) -> id{1,#}(x5)
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs) ->
     map{2,#}(f,cons2(x,xs)) -> app#(f,x)
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs) ->
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
     add{2,#}(s1(x),y) -> add{2,#}(x,y) ->
     add{2,#}(s1(x),y) -> add{2,#}(x,y)
     add{2,#}(s1(x),y) -> add{2,#}(x,y) -> add{2,#}(0(),x6) -> id{1,#}(x6)
    SCC Processor:
     #sccs: 2
     #rules: 4
     #arcs: 12/64
     DPs:
      app#(map1(x4),x5) -> map{2,#}(x4,x5)
      map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
      map{2,#}(f,cons2(x,xs)) -> app#(f,x)
     TRS:
      id1(x) -> x
      add2(0(),x6) -> id1(x6)
      add1(0()) -> id()
      add2(s1(x),y) -> s1(add2(x,y))
      map2(f,nil()) -> nil()
      map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
      app(id(),x5) -> id1(x5)
      app(add1(x4),x5) -> add2(x4,x5)
      app(add(),x5) -> add1(x5)
      app(s(),x5) -> s1(x5)
      app(map1(x4),x5) -> map2(x4,x5)
      app(map(),x5) -> map1(x5)
      app(cons1(x4),x5) -> cons2(x4,x5)
      app(cons(),x5) -> cons1(x5)
     Subterm Criterion Processor:
      simple projection:
       pi(map{2,#}) = 1
       pi(app#) = 1
      problem:
       DPs:
        app#(map1(x4),x5) -> map{2,#}(x4,x5)
       TRS:
        id1(x) -> x
        add2(0(),x6) -> id1(x6)
        add1(0()) -> id()
        add2(s1(x),y) -> s1(add2(x,y))
        map2(f,nil()) -> nil()
        map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
        app(id(),x5) -> id1(x5)
        app(add1(x4),x5) -> add2(x4,x5)
        app(add(),x5) -> add1(x5)
        app(s(),x5) -> s1(x5)
        app(map1(x4),x5) -> map2(x4,x5)
        app(map(),x5) -> map1(x5)
        app(cons1(x4),x5) -> cons2(x4,x5)
        app(cons(),x5) -> cons1(x5)
      SCC Processor:
       #sccs: 0
       #rules: 0
       #arcs: 5/1
       
     
     DPs:
      add{2,#}(s1(x),y) -> add{2,#}(x,y)
     TRS:
      id1(x) -> x
      add2(0(),x6) -> id1(x6)
      add1(0()) -> id()
      add2(s1(x),y) -> s1(add2(x,y))
      map2(f,nil()) -> nil()
      map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
      app(id(),x5) -> id1(x5)
      app(add1(x4),x5) -> add2(x4,x5)
      app(add(),x5) -> add1(x5)
      app(s(),x5) -> s1(x5)
      app(map1(x4),x5) -> map2(x4,x5)
      app(map(),x5) -> map1(x5)
      app(cons1(x4),x5) -> cons2(x4,x5)
      app(cons(),x5) -> cons1(x5)
     Subterm Criterion Processor:
      simple projection:
       pi(add{2,#}) = 0
      problem:
       DPs:
        
       TRS:
        id1(x) -> x
        add2(0(),x6) -> id1(x6)
        add1(0()) -> id()
        add2(s1(x),y) -> s1(add2(x,y))
        map2(f,nil()) -> nil()
        map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
        app(id(),x5) -> id1(x5)
        app(add1(x4),x5) -> add2(x4,x5)
        app(add(),x5) -> add1(x5)
        app(s(),x5) -> s1(x5)
        app(map1(x4),x5) -> map2(x4,x5)
        app(map(),x5) -> map1(x5)
        app(cons1(x4),x5) -> cons2(x4,x5)
        app(cons(),x5) -> cons1(x5)
      Qed