YES

Problem:
 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(flatten(),app(app(node(),x),xs)) ->
 app(app(cons(),x),app(concat(),app(app(map(),flatten()),xs)))
 app(concat(),nil()) -> nil()
 app(concat(),app(app(cons(),x),xs)) -> app(app(append(),x),app(concat(),xs))
 app(app(append(),nil()),xs) -> xs
 app(app(append(),app(app(cons(),x),xs)),ys) -> app(app(cons(),x),app(app(append(),xs),ys))

Proof:
 Uncurry Processor:
  map2(f,nil()) -> nil()
  map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
  flatten1(node2(x,xs)) -> cons2(x,concat1(map2(flatten(),xs)))
  concat1(nil()) -> nil()
  concat1(cons2(x,xs)) -> append2(x,concat1(xs))
  append2(nil(),xs) -> xs
  append2(cons2(x,xs),ys) -> cons2(x,append2(xs,ys))
  app(map1(x4),x5) -> map2(x4,x5)
  app(map(),x5) -> map1(x5)
  app(cons1(x4),x5) -> cons2(x4,x5)
  app(cons(),x5) -> cons1(x5)
  app(flatten(),x5) -> flatten1(x5)
  app(node1(x4),x5) -> node2(x4,x5)
  app(node(),x5) -> node1(x5)
  app(concat(),x5) -> concat1(x5)
  app(append1(x4),x5) -> append2(x4,x5)
  app(append(),x5) -> append1(x5)
  DP Processor:
   DPs:
    map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
    map{2,#}(f,cons2(x,xs)) -> app#(f,x)
    flatten{1,#}(node2(x,xs)) -> map{2,#}(flatten(),xs)
    flatten{1,#}(node2(x,xs)) -> concat{1,#}(map2(flatten(),xs))
    concat{1,#}(cons2(x,xs)) -> concat{1,#}(xs)
    concat{1,#}(cons2(x,xs)) -> append{2,#}(x,concat1(xs))
    append{2,#}(cons2(x,xs),ys) -> append{2,#}(xs,ys)
    app#(map1(x4),x5) -> map{2,#}(x4,x5)
    app#(flatten(),x5) -> flatten{1,#}(x5)
    app#(concat(),x5) -> concat{1,#}(x5)
    app#(append1(x4),x5) -> append{2,#}(x4,x5)
   TRS:
    map2(f,nil()) -> nil()
    map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
    flatten1(node2(x,xs)) -> cons2(x,concat1(map2(flatten(),xs)))
    concat1(nil()) -> nil()
    concat1(cons2(x,xs)) -> append2(x,concat1(xs))
    append2(nil(),xs) -> xs
    append2(cons2(x,xs),ys) -> cons2(x,append2(xs,ys))
    app(map1(x4),x5) -> map2(x4,x5)
    app(map(),x5) -> map1(x5)
    app(cons1(x4),x5) -> cons2(x4,x5)
    app(cons(),x5) -> cons1(x5)
    app(flatten(),x5) -> flatten1(x5)
    app(node1(x4),x5) -> node2(x4,x5)
    app(node(),x5) -> node1(x5)
    app(concat(),x5) -> concat1(x5)
    app(append1(x4),x5) -> append2(x4,x5)
    app(append(),x5) -> append1(x5)
   TDG Processor:
    DPs:
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x)
     flatten{1,#}(node2(x,xs)) -> map{2,#}(flatten(),xs)
     flatten{1,#}(node2(x,xs)) -> concat{1,#}(map2(flatten(),xs))
     concat{1,#}(cons2(x,xs)) -> concat{1,#}(xs)
     concat{1,#}(cons2(x,xs)) -> append{2,#}(x,concat1(xs))
     append{2,#}(cons2(x,xs),ys) -> append{2,#}(xs,ys)
     app#(map1(x4),x5) -> map{2,#}(x4,x5)
     app#(flatten(),x5) -> flatten{1,#}(x5)
     app#(concat(),x5) -> concat{1,#}(x5)
     app#(append1(x4),x5) -> append{2,#}(x4,x5)
    TRS:
     map2(f,nil()) -> nil()
     map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
     flatten1(node2(x,xs)) -> cons2(x,concat1(map2(flatten(),xs)))
     concat1(nil()) -> nil()
     concat1(cons2(x,xs)) -> append2(x,concat1(xs))
     append2(nil(),xs) -> xs
     append2(cons2(x,xs),ys) -> cons2(x,append2(xs,ys))
     app(map1(x4),x5) -> map2(x4,x5)
     app(map(),x5) -> map1(x5)
     app(cons1(x4),x5) -> cons2(x4,x5)
     app(cons(),x5) -> cons1(x5)
     app(flatten(),x5) -> flatten1(x5)
     app(node1(x4),x5) -> node2(x4,x5)
     app(node(),x5) -> node1(x5)
     app(concat(),x5) -> concat1(x5)
     app(append1(x4),x5) -> append2(x4,x5)
     app(append(),x5) -> append1(x5)
    graph:
     append{2,#}(cons2(x,xs),ys) -> append{2,#}(xs,ys) ->
     append{2,#}(cons2(x,xs),ys) -> append{2,#}(xs,ys)
     concat{1,#}(cons2(x,xs)) -> append{2,#}(x,concat1(xs)) ->
     append{2,#}(cons2(x,xs),ys) -> append{2,#}(xs,ys)
     concat{1,#}(cons2(x,xs)) -> concat{1,#}(xs) ->
     concat{1,#}(cons2(x,xs)) -> append{2,#}(x,concat1(xs))
     concat{1,#}(cons2(x,xs)) -> concat{1,#}(xs) ->
     concat{1,#}(cons2(x,xs)) -> concat{1,#}(xs)
     flatten{1,#}(node2(x,xs)) -> concat{1,#}(map2(flatten(),xs)) ->
     concat{1,#}(cons2(x,xs)) -> append{2,#}(x,concat1(xs))
     flatten{1,#}(node2(x,xs)) -> concat{1,#}(map2(flatten(),xs)) ->
     concat{1,#}(cons2(x,xs)) -> concat{1,#}(xs)
     flatten{1,#}(node2(x,xs)) -> map{2,#}(flatten(),xs) ->
     map{2,#}(f,cons2(x,xs)) -> app#(f,x)
     flatten{1,#}(node2(x,xs)) -> map{2,#}(flatten(),xs) ->
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
     app#(append1(x4),x5) -> append{2,#}(x4,x5) ->
     append{2,#}(cons2(x,xs),ys) -> append{2,#}(xs,ys)
     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#(concat(),x5) -> concat{1,#}(x5) ->
     concat{1,#}(cons2(x,xs)) -> append{2,#}(x,concat1(xs))
     app#(concat(),x5) -> concat{1,#}(x5) ->
     concat{1,#}(cons2(x,xs)) -> concat{1,#}(xs)
     app#(flatten(),x5) -> flatten{1,#}(x5) ->
     flatten{1,#}(node2(x,xs)) -> concat{1,#}(map2(flatten(),xs))
     app#(flatten(),x5) -> flatten{1,#}(x5) ->
     flatten{1,#}(node2(x,xs)) -> map{2,#}(flatten(),xs)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(append1(x4),x5) -> append{2,#}(x4,x5)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(concat(),x5) -> concat{1,#}(x5)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(flatten(),x5) -> flatten{1,#}(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) ->
     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)
    SCC Processor:
     #sccs: 3
     #rules: 7
     #arcs: 21/121
     DPs:
      flatten{1,#}(node2(x,xs)) -> map{2,#}(flatten(),xs)
      map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
      map{2,#}(f,cons2(x,xs)) -> app#(f,x)
      app#(map1(x4),x5) -> map{2,#}(x4,x5)
      app#(flatten(),x5) -> flatten{1,#}(x5)
     TRS:
      map2(f,nil()) -> nil()
      map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
      flatten1(node2(x,xs)) -> cons2(x,concat1(map2(flatten(),xs)))
      concat1(nil()) -> nil()
      concat1(cons2(x,xs)) -> append2(x,concat1(xs))
      append2(nil(),xs) -> xs
      append2(cons2(x,xs),ys) -> cons2(x,append2(xs,ys))
      app(map1(x4),x5) -> map2(x4,x5)
      app(map(),x5) -> map1(x5)
      app(cons1(x4),x5) -> cons2(x4,x5)
      app(cons(),x5) -> cons1(x5)
      app(flatten(),x5) -> flatten1(x5)
      app(node1(x4),x5) -> node2(x4,x5)
      app(node(),x5) -> node1(x5)
      app(concat(),x5) -> concat1(x5)
      app(append1(x4),x5) -> append2(x4,x5)
      app(append(),x5) -> append1(x5)
     Subterm Criterion Processor:
      simple projection:
       pi(map{2,#}) = 1
       pi(app#) = 1
       pi(flatten{1,#}) = 0
      problem:
       DPs:
        app#(map1(x4),x5) -> map{2,#}(x4,x5)
        app#(flatten(),x5) -> flatten{1,#}(x5)
       TRS:
        map2(f,nil()) -> nil()
        map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
        flatten1(node2(x,xs)) -> cons2(x,concat1(map2(flatten(),xs)))
        concat1(nil()) -> nil()
        concat1(cons2(x,xs)) -> append2(x,concat1(xs))
        append2(nil(),xs) -> xs
        append2(cons2(x,xs),ys) -> cons2(x,append2(xs,ys))
        app(map1(x4),x5) -> map2(x4,x5)
        app(map(),x5) -> map1(x5)
        app(cons1(x4),x5) -> cons2(x4,x5)
        app(cons(),x5) -> cons1(x5)
        app(flatten(),x5) -> flatten1(x5)
        app(node1(x4),x5) -> node2(x4,x5)
        app(node(),x5) -> node1(x5)
        app(concat(),x5) -> concat1(x5)
        app(append1(x4),x5) -> append2(x4,x5)
        app(append(),x5) -> append1(x5)
      SCC Processor:
       #sccs: 0
       #rules: 0
       #arcs: 9/4
       
     
     DPs:
      concat{1,#}(cons2(x,xs)) -> concat{1,#}(xs)
     TRS:
      map2(f,nil()) -> nil()
      map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
      flatten1(node2(x,xs)) -> cons2(x,concat1(map2(flatten(),xs)))
      concat1(nil()) -> nil()
      concat1(cons2(x,xs)) -> append2(x,concat1(xs))
      append2(nil(),xs) -> xs
      append2(cons2(x,xs),ys) -> cons2(x,append2(xs,ys))
      app(map1(x4),x5) -> map2(x4,x5)
      app(map(),x5) -> map1(x5)
      app(cons1(x4),x5) -> cons2(x4,x5)
      app(cons(),x5) -> cons1(x5)
      app(flatten(),x5) -> flatten1(x5)
      app(node1(x4),x5) -> node2(x4,x5)
      app(node(),x5) -> node1(x5)
      app(concat(),x5) -> concat1(x5)
      app(append1(x4),x5) -> append2(x4,x5)
      app(append(),x5) -> append1(x5)
     Subterm Criterion Processor:
      simple projection:
       pi(concat{1,#}) = 0
      problem:
       DPs:
        
       TRS:
        map2(f,nil()) -> nil()
        map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
        flatten1(node2(x,xs)) -> cons2(x,concat1(map2(flatten(),xs)))
        concat1(nil()) -> nil()
        concat1(cons2(x,xs)) -> append2(x,concat1(xs))
        append2(nil(),xs) -> xs
        append2(cons2(x,xs),ys) -> cons2(x,append2(xs,ys))
        app(map1(x4),x5) -> map2(x4,x5)
        app(map(),x5) -> map1(x5)
        app(cons1(x4),x5) -> cons2(x4,x5)
        app(cons(),x5) -> cons1(x5)
        app(flatten(),x5) -> flatten1(x5)
        app(node1(x4),x5) -> node2(x4,x5)
        app(node(),x5) -> node1(x5)
        app(concat(),x5) -> concat1(x5)
        app(append1(x4),x5) -> append2(x4,x5)
        app(append(),x5) -> append1(x5)
      Qed
     
     DPs:
      append{2,#}(cons2(x,xs),ys) -> append{2,#}(xs,ys)
     TRS:
      map2(f,nil()) -> nil()
      map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
      flatten1(node2(x,xs)) -> cons2(x,concat1(map2(flatten(),xs)))
      concat1(nil()) -> nil()
      concat1(cons2(x,xs)) -> append2(x,concat1(xs))
      append2(nil(),xs) -> xs
      append2(cons2(x,xs),ys) -> cons2(x,append2(xs,ys))
      app(map1(x4),x5) -> map2(x4,x5)
      app(map(),x5) -> map1(x5)
      app(cons1(x4),x5) -> cons2(x4,x5)
      app(cons(),x5) -> cons1(x5)
      app(flatten(),x5) -> flatten1(x5)
      app(node1(x4),x5) -> node2(x4,x5)
      app(node(),x5) -> node1(x5)
      app(concat(),x5) -> concat1(x5)
      app(append1(x4),x5) -> append2(x4,x5)
      app(append(),x5) -> append1(x5)
     Subterm Criterion Processor:
      simple projection:
       pi(append{2,#}) = 0
      problem:
       DPs:
        
       TRS:
        map2(f,nil()) -> nil()
        map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
        flatten1(node2(x,xs)) -> cons2(x,concat1(map2(flatten(),xs)))
        concat1(nil()) -> nil()
        concat1(cons2(x,xs)) -> append2(x,concat1(xs))
        append2(nil(),xs) -> xs
        append2(cons2(x,xs),ys) -> cons2(x,append2(xs,ys))
        app(map1(x4),x5) -> map2(x4,x5)
        app(map(),x5) -> map1(x5)
        app(cons1(x4),x5) -> cons2(x4,x5)
        app(cons(),x5) -> cons1(x5)
        app(flatten(),x5) -> flatten1(x5)
        app(node1(x4),x5) -> node2(x4,x5)
        app(node(),x5) -> node1(x5)
        app(concat(),x5) -> concat1(x5)
        app(append1(x4),x5) -> append2(x4,x5)
        app(append(),x5) -> append1(x5)
      Qed