YES
Input TRS:
      1: app(app(map(),f),nil()) -> nil()
      2: app(app(map(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(f,x)),app(app(map(),f),xs))
      3: app(app(treemap(),f),app(app(node(),x),xs)) -> app(app(node(),app(f,x)),app(app(map(),app(treemap(),f)),xs))
Number of strict rules: 3
Direct POLO(bPol) ... failed.
Uncurrying app
      1: app^2_map(f,nil()) -> nil()
      2: app^2_map(f,app^2_cons(x,xs)) -> app^2_cons(app(f,x),app^2_map(f,xs))
      3: app^2_treemap(f,app^2_node(x,xs)) -> app^2_node(app(f,x),app^2_map(app^1_treemap(f),xs))
      4: app(treemap(),_1) ->= app^1_treemap(_1)
      5: app(app^1_treemap(_1),_2) ->= app^2_treemap(_1,_2)
      6: app(cons(),_1) ->= app^1_cons(_1)
      7: app(app^1_cons(_1),_2) ->= app^2_cons(_1,_2)
      8: app(map(),_1) ->= app^1_map(_1)
      9: app(app^1_map(_1),_2) ->= app^2_map(_1,_2)
      10: app(node(),_1) ->= app^1_node(_1)
      11: app(app^1_node(_1),_2) ->= app^2_node(_1,_2)
Number of strict rules: 3
Direct POLO(bPol) ... failed.
Dependency Pairs:
     #1: #app^2_map(f,app^2_cons(x,xs)) -> #app(f,x)
     #2: #app^2_map(f,app^2_cons(x,xs)) -> #app^2_map(f,xs)
     #3: #app(app^1_map(_1),_2) ->? #app^2_map(_1,_2)
     #4: #app(app^1_treemap(_1),_2) ->? #app^2_treemap(_1,_2)
     #5: #app^2_treemap(f,app^2_node(x,xs)) -> #app(f,x)
     #6: #app^2_treemap(f,app^2_node(x,xs)) -> #app^2_map(app^1_treemap(f),xs)
Number of SCCs: 1, DPs: 6
  SCC { #1..6 }
POLO(Sum)... succeeded.
      app^1_cons	w: 0
      #app^2_map	w: x2
      app^2_node	w: x1 + x2 + 2
      nil	w: 0
      app^1_treemap	w: 1
      app^2_treemap	w: 0
      #app	w: x2 + 1
      map	w: 0
      treemap	w: 0
      cons	w: 0
      #app^2_treemap	w: x2
      app^1_map	w: 1
      app^2_cons	w: x1 + x2 + 40
      node	w: 0
      app^2_map	w: 0
      app	w: 0
      app^1_node	w: 0
    USABLE RULES: { }
    Removed DPs: #1..6
Number of SCCs: 0, DPs: 0