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(append(),xs),nil()) -> xs
      4: app(app(append(),nil()),ys) -> ys
      5: app(app(append(),app(app(cons(),x),xs)),ys) -> app(app(cons(),x),app(app(append(),xs),ys))
      6: app(app(zip(),nil()),yss) -> yss
      7: app(app(zip(),xss),nil()) -> xss
      8: app(app(zip(),app(app(cons(),xs),xss)),app(app(cons(),ys),yss)) -> app(app(cons(),app(app(append(),xs),ys)),app(app(zip(),xss),yss))
      9: app(app(combine(),xs),nil()) -> xs
      10: app(app(combine(),xs),app(app(cons(),ys),yss)) -> app(app(combine(),app(app(zip(),xs),ys)),yss)
      11: app(levels(),app(app(node(),x),xs)) -> app(app(cons(),app(app(cons(),x),nil())),app(app(combine(),nil()),app(app(map(),levels()),xs)))
Number of strict rules: 11
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_append(xs,nil()) -> xs
      4: app^2_append(nil(),ys) -> ys
      5: app^2_append(app^2_cons(x,xs),ys) -> app^2_cons(x,app^2_append(xs,ys))
      6: app^2_zip(nil(),yss) -> yss
      7: app^2_zip(xss,nil()) -> xss
      8: app^2_zip(app^2_cons(xs,xss),app^2_cons(ys,yss)) -> app^2_cons(app^2_append(xs,ys),app^2_zip(xss,yss))
      9: app^2_combine(xs,nil()) -> xs
      10: app^2_combine(xs,app^2_cons(ys,yss)) -> app^2_combine(app^2_zip(xs,ys),yss)
      11: app^1_levels(app^2_node(x,xs)) -> app^2_cons(app^2_cons(x,nil()),app^2_combine(nil(),app^2_map(levels(),xs)))
      12: app(append(),_1) ->= app^1_append(_1)
      13: app(app^1_append(_1),_2) ->= app^2_append(_1,_2)
      14: app(combine(),_1) ->= app^1_combine(_1)
      15: app(app^1_combine(_1),_2) ->= app^2_combine(_1,_2)
      16: app(levels(),_1) ->= app^1_levels(_1)
      17: app(cons(),_1) ->= app^1_cons(_1)
      18: app(app^1_cons(_1),_2) ->= app^2_cons(_1,_2)
      19: app(map(),_1) ->= app^1_map(_1)
      20: app(app^1_map(_1),_2) ->= app^2_map(_1,_2)
      21: app(zip(),_1) ->= app^1_zip(_1)
      22: app(app^1_zip(_1),_2) ->= app^2_zip(_1,_2)
      23: app(node(),_1) ->= app^1_node(_1)
      24: app(app^1_node(_1),_2) ->= app^2_node(_1,_2)
Number of strict rules: 11
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_append(_1),_2) ->? #app^2_append(_1,_2)
     #4: #app^1_levels(app^2_node(x,xs)) -> #app^2_combine(nil(),app^2_map(levels(),xs))
     #5: #app^1_levels(app^2_node(x,xs)) -> #app^2_map(levels(),xs)
     #6: #app(app^1_map(_1),_2) ->? #app^2_map(_1,_2)
     #7: #app^2_combine(xs,app^2_cons(ys,yss)) -> #app^2_combine(app^2_zip(xs,ys),yss)
     #8: #app^2_combine(xs,app^2_cons(ys,yss)) -> #app^2_zip(xs,ys)
     #9: #app^2_append(app^2_cons(x,xs),ys) -> #app^2_append(xs,ys)
     #10: #app(app^1_zip(_1),_2) ->? #app^2_zip(_1,_2)
     #11: #app(levels(),_1) ->? #app^1_levels(_1)
     #12: #app^2_zip(app^2_cons(xs,xss),app^2_cons(ys,yss)) -> #app^2_append(xs,ys)
     #13: #app^2_zip(app^2_cons(xs,xss),app^2_cons(ys,yss)) -> #app^2_zip(xss,yss)
     #14: #app(app^1_combine(_1),_2) ->? #app^2_combine(_1,_2)
Number of SCCs: 4, DPs: 8
  SCC { #9 }
POLO(Sum)... succeeded.
      app^2_zip	w: 0
      app^1_cons	w: 0
      #app^2_map	w: 0
      app^1_combine	w: 0
      app^1_append	w: 0
      app^1_zip	w: 0
      #app^2_zip	w: 0
      #app^2_append	w: x1
      app^2_node	w: 0
      append	w: 0
      combine	w: 0
      levels	w: 0
      nil	w: 0
      #app	w: 0
      map	w: 0
      app^2_combine	w: 0
      #app^1_levels	w: 0
      cons	w: 0
      app^1_levels	w: 0
      app^1_map	w: 0
      app^2_cons	w: x2 + 1
      zip	w: 0
      node	w: 0
      app^2_append	w: 0
      app^2_map	w: 0
      #app^2_combine	w: 0
      app	w: 0
      app^1_node	w: 0
    USABLE RULES: { }
    Removed DPs: #9
Number of SCCs: 3, DPs: 7
  SCC { #7 }
POLO(Sum)... succeeded.
      app^2_zip	w: x1 + 1
      app^1_cons	w: 0
      #app^2_map	w: 0
      app^1_combine	w: 0
      app^1_append	w: 0
      app^1_zip	w: 0
      #app^2_zip	w: 0
      #app^2_append	w: 0
      app^2_node	w: 0
      append	w: 0
      combine	w: 0
      levels	w: 0
      nil	w: 1
      #app	w: 0
      map	w: 0
      app^2_combine	w: 0
      #app^1_levels	w: 0
      cons	w: 0
      app^1_levels	w: 0
      app^1_map	w: 0
      app^2_cons	w: x2 + 2438
      zip	w: 0
      node	w: 0
      app^2_append	w: x1 + x2 + 20653
      app^2_map	w: 0
      #app^2_combine	w: x2
      app	w: 0
      app^1_node	w: 0
    USABLE RULES: { }
    Removed DPs: #7
Number of SCCs: 2, DPs: 6
  SCC { #13 }
POLO(Sum)... succeeded.
      app^2_zip	w: x1 + 1
      app^1_cons	w: 0
      #app^2_map	w: 0
      app^1_combine	w: 0
      app^1_append	w: 0
      app^1_zip	w: 0
      #app^2_zip	w: x1
      #app^2_append	w: 0
      app^2_node	w: 0
      append	w: 0
      combine	w: 0
      levels	w: 0
      nil	w: 1
      #app	w: 0
      map	w: 0
      app^2_combine	w: 0
      #app^1_levels	w: 0
      cons	w: 0
      app^1_levels	w: 0
      app^1_map	w: 0
      app^2_cons	w: x2 + 2438
      zip	w: 0
      node	w: 0
      app^2_append	w: x1 + x2 + 42736
      app^2_map	w: 0
      #app^2_combine	w: 0
      app	w: 0
      app^1_node	w: 0
    USABLE RULES: { }
    Removed DPs: #13
Number of SCCs: 1, DPs: 5
  SCC { #1 #2 #5 #6 #11 }
POLO(Sum)... succeeded.
      app^2_zip	w: x1 + 1
      app^1_cons	w: 0
      #app^2_map	w: x1
      app^1_combine	w: 0
      app^1_append	w: 0
      app^1_zip	w: 0
      #app^2_zip	w: 0
      #app^2_append	w: 0
      app^2_node	w: 1
      append	w: 0
      combine	w: 0
      levels	w: 1
      nil	w: 1
      #app	w: x1
      map	w: 0
      app^2_combine	w: 0
      #app^1_levels	w: 1
      cons	w: 0
      app^1_levels	w: 0
      app^1_map	w: x1 + 1
      app^2_cons	w: x2 + 2438
      zip	w: 0
      node	w: 0
      app^2_append	w: x1 + x2 + 1
      app^2_map	w: 0
      #app^2_combine	w: 0
      app	w: 0
      app^1_node	w: 0
    USABLE RULES: { }
    Removed DPs: #6
Number of SCCs: 1, DPs: 4
  SCC { #1 #2 #5 #11 }
POLO(Sum)... succeeded.
      app^2_zip	w: x1 + 1
      app^1_cons	w: 0
      #app^2_map	w: x1 + x2
      app^1_combine	w: 0
      app^1_append	w: 0
      app^1_zip	w: 0
      #app^2_zip	w: 0
      #app^2_append	w: 0
      app^2_node	w: x2 + 2
      append	w: 0
      combine	w: 0
      levels	w: 1424
      nil	w: 1
      #app	w: x1 + x2
      map	w: 0
      app^2_combine	w: 0
      #app^1_levels	w: x1 + 1423
      cons	w: 0
      app^1_levels	w: 0
      app^1_map	w: 1
      app^2_cons	w: x1 + x2 + 1
      zip	w: 0
      node	w: 0
      app^2_append	w: x1 + x2
      app^2_map	w: 0
      #app^2_combine	w: 0
      app	w: 0
      app^1_node	w: 0
    USABLE RULES: { 3..5 }
    Removed DPs: #1 #2 #5 #11
Number of SCCs: 0, DPs: 0