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(app(treemap(),f),app(app(node(),x),xs)) ->
 app(app(node(),app(f,x)),app(app(map(),app(treemap(),f)),xs))

Proof:
 Uncurry Processor:
  map2(f,nil()) -> nil()
  map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
  treemap2(f,node2(x,xs)) -> node2(app(f,x),map2(treemap1(f),xs))
  app(map1(x3),x4) -> map2(x3,x4)
  app(map(),x4) -> map1(x4)
  app(cons1(x3),x4) -> cons2(x3,x4)
  app(cons(),x4) -> cons1(x4)
  app(treemap1(x3),x4) -> treemap2(x3,x4)
  app(treemap(),x4) -> treemap1(x4)
  app(node1(x3),x4) -> node2(x3,x4)
  app(node(),x4) -> node1(x4)
  DP Processor:
   DPs:
    map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
    map{2,#}(f,cons2(x,xs)) -> app#(f,x)
    treemap{2,#}(f,node2(x,xs)) -> map{2,#}(treemap1(f),xs)
    treemap{2,#}(f,node2(x,xs)) -> app#(f,x)
    app#(map1(x3),x4) -> map{2,#}(x3,x4)
    app#(treemap1(x3),x4) -> treemap{2,#}(x3,x4)
   TRS:
    map2(f,nil()) -> nil()
    map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
    treemap2(f,node2(x,xs)) -> node2(app(f,x),map2(treemap1(f),xs))
    app(map1(x3),x4) -> map2(x3,x4)
    app(map(),x4) -> map1(x4)
    app(cons1(x3),x4) -> cons2(x3,x4)
    app(cons(),x4) -> cons1(x4)
    app(treemap1(x3),x4) -> treemap2(x3,x4)
    app(treemap(),x4) -> treemap1(x4)
    app(node1(x3),x4) -> node2(x3,x4)
    app(node(),x4) -> node1(x4)
   TDG Processor:
    DPs:
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x)
     treemap{2,#}(f,node2(x,xs)) -> map{2,#}(treemap1(f),xs)
     treemap{2,#}(f,node2(x,xs)) -> app#(f,x)
     app#(map1(x3),x4) -> map{2,#}(x3,x4)
     app#(treemap1(x3),x4) -> treemap{2,#}(x3,x4)
    TRS:
     map2(f,nil()) -> nil()
     map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
     treemap2(f,node2(x,xs)) -> node2(app(f,x),map2(treemap1(f),xs))
     app(map1(x3),x4) -> map2(x3,x4)
     app(map(),x4) -> map1(x4)
     app(cons1(x3),x4) -> cons2(x3,x4)
     app(cons(),x4) -> cons1(x4)
     app(treemap1(x3),x4) -> treemap2(x3,x4)
     app(treemap(),x4) -> treemap1(x4)
     app(node1(x3),x4) -> node2(x3,x4)
     app(node(),x4) -> node1(x4)
    graph:
     treemap{2,#}(f,node2(x,xs)) -> app#(f,x) ->
     app#(treemap1(x3),x4) -> treemap{2,#}(x3,x4)
     treemap{2,#}(f,node2(x,xs)) -> app#(f,x) ->
     app#(map1(x3),x4) -> map{2,#}(x3,x4)
     treemap{2,#}(f,node2(x,xs)) -> map{2,#}(treemap1(f),xs) ->
     map{2,#}(f,cons2(x,xs)) -> app#(f,x)
     treemap{2,#}(f,node2(x,xs)) -> map{2,#}(treemap1(f),xs) ->
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
     app#(treemap1(x3),x4) -> treemap{2,#}(x3,x4) ->
     treemap{2,#}(f,node2(x,xs)) -> app#(f,x)
     app#(treemap1(x3),x4) -> treemap{2,#}(x3,x4) ->
     treemap{2,#}(f,node2(x,xs)) -> map{2,#}(treemap1(f),xs)
     app#(map1(x3),x4) -> map{2,#}(x3,x4) ->
     map{2,#}(f,cons2(x,xs)) -> app#(f,x)
     app#(map1(x3),x4) -> map{2,#}(x3,x4) ->
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(treemap1(x3),x4) -> treemap{2,#}(x3,x4)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(map1(x3),x4) -> map{2,#}(x3,x4)
     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)
    Subterm Criterion Processor:
     simple projection:
      pi(map{2,#}) = 1
      pi(app#) = 1
      pi(treemap{2,#}) = 1
     problem:
      DPs:
       app#(map1(x3),x4) -> map{2,#}(x3,x4)
       app#(treemap1(x3),x4) -> treemap{2,#}(x3,x4)
      TRS:
       map2(f,nil()) -> nil()
       map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
       treemap2(f,node2(x,xs)) -> node2(app(f,x),map2(treemap1(f),xs))
       app(map1(x3),x4) -> map2(x3,x4)
       app(map(),x4) -> map1(x4)
       app(cons1(x3),x4) -> cons2(x3,x4)
       app(cons(),x4) -> cons1(x4)
       app(treemap1(x3),x4) -> treemap2(x3,x4)
       app(treemap(),x4) -> treemap1(x4)
       app(node1(x3),x4) -> node2(x3,x4)
       app(node(),x4) -> node1(x4)
     SCC Processor:
      #sccs: 0
      #rules: 0
      #arcs: 12/4