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(le(),0()),y) -> true()
 app(app(le(),app(s(),x)),0()) -> false()
 app(app(le(),app(s(),x)),app(s(),y)) -> app(app(le(),x),y)
 app(app(maxlist(),x),app(app(cons(),y),ys)) ->
 app(app(if(),app(app(le(),x),y)),app(app(maxlist(),y),ys))
 app(app(maxlist(),x),nil()) -> x
 app(height(),app(app(node(),x),xs)) ->
 app(s(),app(app(maxlist(),0()),app(app(map(),height()),xs)))

Proof:
 DP Processor:
  DPs:
   app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs)
   app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x)
   app#(app(map(),f),app(app(cons(),x),xs)) -> app#(cons(),app(f,x))
   app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(cons(),app(f,x)),app(app(map(),f),xs))
   app#(app(le(),app(s(),x)),app(s(),y)) -> app#(le(),x)
   app#(app(le(),app(s(),x)),app(s(),y)) -> app#(app(le(),x),y)
   app#(app(maxlist(),x),app(app(cons(),y),ys)) -> app#(maxlist(),y)
   app#(app(maxlist(),x),app(app(cons(),y),ys)) -> app#(app(maxlist(),y),ys)
   app#(app(maxlist(),x),app(app(cons(),y),ys)) -> app#(le(),x)
   app#(app(maxlist(),x),app(app(cons(),y),ys)) -> app#(app(le(),x),y)
   app#(app(maxlist(),x),app(app(cons(),y),ys)) -> app#(if(),app(app(le(),x),y))
   app#(app(maxlist(),x),app(app(cons(),y),ys)) ->
   app#(app(if(),app(app(le(),x),y)),app(app(maxlist(),y),ys))
   app#(height(),app(app(node(),x),xs)) -> app#(map(),height())
   app#(height(),app(app(node(),x),xs)) -> app#(app(map(),height()),xs)
   app#(height(),app(app(node(),x),xs)) -> app#(maxlist(),0())
   app#(height(),app(app(node(),x),xs)) -> app#(app(maxlist(),0()),app(app(map(),height()),xs))
   app#(height(),app(app(node(),x),xs)) ->
   app#(s(),app(app(maxlist(),0()),app(app(map(),height()),xs)))
  TRS:
   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(le(),0()),y) -> true()
   app(app(le(),app(s(),x)),0()) -> false()
   app(app(le(),app(s(),x)),app(s(),y)) -> app(app(le(),x),y)
   app(app(maxlist(),x),app(app(cons(),y),ys)) ->
   app(app(if(),app(app(le(),x),y)),app(app(maxlist(),y),ys))
   app(app(maxlist(),x),nil()) -> x
   app(height(),app(app(node(),x),xs)) ->
   app(s(),app(app(maxlist(),0()),app(app(map(),height()),xs)))
  EDG Processor:
   DPs:
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(cons(),app(f,x))
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(cons(),app(f,x)),app(app(map(),f),xs))
    app#(app(le(),app(s(),x)),app(s(),y)) -> app#(le(),x)
    app#(app(le(),app(s(),x)),app(s(),y)) -> app#(app(le(),x),y)
    app#(app(maxlist(),x),app(app(cons(),y),ys)) -> app#(maxlist(),y)
    app#(app(maxlist(),x),app(app(cons(),y),ys)) -> app#(app(maxlist(),y),ys)
    app#(app(maxlist(),x),app(app(cons(),y),ys)) -> app#(le(),x)
    app#(app(maxlist(),x),app(app(cons(),y),ys)) -> app#(app(le(),x),y)
    app#(app(maxlist(),x),app(app(cons(),y),ys)) -> app#(if(),app(app(le(),x),y))
    app#(app(maxlist(),x),app(app(cons(),y),ys)) ->
    app#(app(if(),app(app(le(),x),y)),app(app(maxlist(),y),ys))
    app#(height(),app(app(node(),x),xs)) -> app#(map(),height())
    app#(height(),app(app(node(),x),xs)) -> app#(app(map(),height()),xs)
    app#(height(),app(app(node(),x),xs)) -> app#(maxlist(),0())
    app#(height(),app(app(node(),x),xs)) -> app#(app(maxlist(),0()),app(app(map(),height()),xs))
    app#(height(),app(app(node(),x),xs)) ->
    app#(s(),app(app(maxlist(),0()),app(app(map(),height()),xs)))
   TRS:
    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(le(),0()),y) -> true()
    app(app(le(),app(s(),x)),0()) -> false()
    app(app(le(),app(s(),x)),app(s(),y)) -> app(app(le(),x),y)
    app(app(maxlist(),x),app(app(cons(),y),ys)) ->
    app(app(if(),app(app(le(),x),y)),app(app(maxlist(),y),ys))
    app(app(maxlist(),x),nil()) -> x
    app(height(),app(app(node(),x),xs)) ->
    app(s(),app(app(maxlist(),0()),app(app(map(),height()),xs)))
   graph:
    app#(height(),app(app(node(),x),xs)) -> app#(app(maxlist(),0()),app(app(map(),height()),xs)) ->
    app#(app(maxlist(),x),app(app(cons(),y),ys)) -> app#(maxlist(),y)
    app#(height(),app(app(node(),x),xs)) -> app#(app(maxlist(),0()),app(app(map(),height()),xs)) ->
    app#(app(maxlist(),x),app(app(cons(),y),ys)) -> app#(app(maxlist(),y),ys)
    app#(height(),app(app(node(),x),xs)) -> app#(app(maxlist(),0()),app(app(map(),height()),xs)) ->
    app#(app(maxlist(),x),app(app(cons(),y),ys)) -> app#(le(),x)
    app#(height(),app(app(node(),x),xs)) -> app#(app(maxlist(),0()),app(app(map(),height()),xs)) ->
    app#(app(maxlist(),x),app(app(cons(),y),ys)) -> app#(app(le(),x),y)
    app#(height(),app(app(node(),x),xs)) -> app#(app(maxlist(),0()),app(app(map(),height()),xs)) ->
    app#(app(maxlist(),x),app(app(cons(),y),ys)) -> app#(if(),app(app(le(),x),y))
    app#(height(),app(app(node(),x),xs)) -> app#(app(maxlist(),0()),app(app(map(),height()),xs)) ->
    app#(app(maxlist(),x),app(app(cons(),y),ys)) ->
    app#(app(if(),app(app(le(),x),y)),app(app(maxlist(),y),ys))
    app#(height(),app(app(node(),x),xs)) -> app#(app(map(),height()),xs) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs)
    app#(height(),app(app(node(),x),xs)) -> app#(app(map(),height()),xs) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x)
    app#(height(),app(app(node(),x),xs)) -> app#(app(map(),height()),xs) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(cons(),app(f,x))
    app#(height(),app(app(node(),x),xs)) -> app#(app(map(),height()),xs) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(cons(),app(f,x)),app(app(map(),f),xs))
    app#(app(maxlist(),x),app(app(cons(),y),ys)) -> app#(app(maxlist(),y),ys) ->
    app#(app(maxlist(),x),app(app(cons(),y),ys)) -> app#(maxlist(),y)
    app#(app(maxlist(),x),app(app(cons(),y),ys)) -> app#(app(maxlist(),y),ys) ->
    app#(app(maxlist(),x),app(app(cons(),y),ys)) -> app#(app(maxlist(),y),ys)
    app#(app(maxlist(),x),app(app(cons(),y),ys)) -> app#(app(maxlist(),y),ys) ->
    app#(app(maxlist(),x),app(app(cons(),y),ys)) -> app#(le(),x)
    app#(app(maxlist(),x),app(app(cons(),y),ys)) -> app#(app(maxlist(),y),ys) ->
    app#(app(maxlist(),x),app(app(cons(),y),ys)) -> app#(app(le(),x),y)
    app#(app(maxlist(),x),app(app(cons(),y),ys)) -> app#(app(maxlist(),y),ys) ->
    app#(app(maxlist(),x),app(app(cons(),y),ys)) -> app#(if(),app(app(le(),x),y))
    app#(app(maxlist(),x),app(app(cons(),y),ys)) -> app#(app(maxlist(),y),ys) ->
    app#(app(maxlist(),x),app(app(cons(),y),ys)) ->
    app#(app(if(),app(app(le(),x),y)),app(app(maxlist(),y),ys))
    app#(app(maxlist(),x),app(app(cons(),y),ys)) -> app#(app(le(),x),y) ->
    app#(app(le(),app(s(),x)),app(s(),y)) -> app#(le(),x)
    app#(app(maxlist(),x),app(app(cons(),y),ys)) -> app#(app(le(),x),y) ->
    app#(app(le(),app(s(),x)),app(s(),y)) -> app#(app(le(),x),y)
    app#(app(le(),app(s(),x)),app(s(),y)) -> app#(app(le(),x),y) ->
    app#(app(le(),app(s(),x)),app(s(),y)) -> app#(le(),x)
    app#(app(le(),app(s(),x)),app(s(),y)) -> app#(app(le(),x),y) ->
    app#(app(le(),app(s(),x)),app(s(),y)) -> app#(app(le(),x),y)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(cons(),app(f,x))
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(cons(),app(f,x)),app(app(map(),f),xs))
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(cons(),app(f,x))
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(cons(),app(f,x)),app(app(map(),f),xs))
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(le(),app(s(),x)),app(s(),y)) -> app#(le(),x)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(le(),app(s(),x)),app(s(),y)) -> app#(app(le(),x),y)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(maxlist(),x),app(app(cons(),y),ys)) -> app#(maxlist(),y)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(maxlist(),x),app(app(cons(),y),ys)) -> app#(app(maxlist(),y),ys)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(maxlist(),x),app(app(cons(),y),ys)) -> app#(le(),x)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(maxlist(),x),app(app(cons(),y),ys)) -> app#(app(le(),x),y)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(maxlist(),x),app(app(cons(),y),ys)) -> app#(if(),app(app(le(),x),y))
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(maxlist(),x),app(app(cons(),y),ys)) ->
    app#(app(if(),app(app(le(),x),y)),app(app(maxlist(),y),ys))
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(height(),app(app(node(),x),xs)) -> app#(map(),height())
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(height(),app(app(node(),x),xs)) -> app#(app(map(),height()),xs)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(height(),app(app(node(),x),xs)) -> app#(maxlist(),0())
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(height(),app(app(node(),x),xs)) -> app#(app(maxlist(),0()),app(app(map(),height()),xs))
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(height(),app(app(node(),x),xs)) ->
    app#(s(),app(app(maxlist(),0()),app(app(map(),height()),xs)))
   SCC Processor:
    #sccs: 3
    #rules: 5
    #arcs: 41/289
    DPs:
     app#(height(),app(app(node(),x),xs)) -> app#(app(map(),height()),xs)
     app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x)
     app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs)
    TRS:
     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(le(),0()),y) -> true()
     app(app(le(),app(s(),x)),0()) -> false()
     app(app(le(),app(s(),x)),app(s(),y)) -> app(app(le(),x),y)
     app(app(maxlist(),x),app(app(cons(),y),ys)) ->
     app(app(if(),app(app(le(),x),y)),app(app(maxlist(),y),ys))
     app(app(maxlist(),x),nil()) -> x
     app(height(),app(app(node(),x),xs)) ->
     app(s(),app(app(maxlist(),0()),app(app(map(),height()),xs)))
    Subterm Criterion Processor:
     simple projection:
      pi(app#) = 1
     problem:
      DPs:
       
      TRS:
       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(le(),0()),y) -> true()
       app(app(le(),app(s(),x)),0()) -> false()
       app(app(le(),app(s(),x)),app(s(),y)) -> app(app(le(),x),y)
       app(app(maxlist(),x),app(app(cons(),y),ys)) ->
       app(app(if(),app(app(le(),x),y)),app(app(maxlist(),y),ys))
       app(app(maxlist(),x),nil()) -> x
       app(height(),app(app(node(),x),xs)) ->
       app(s(),app(app(maxlist(),0()),app(app(map(),height()),xs)))
     Qed
    
    DPs:
     app#(app(maxlist(),x),app(app(cons(),y),ys)) -> app#(app(maxlist(),y),ys)
    TRS:
     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(le(),0()),y) -> true()
     app(app(le(),app(s(),x)),0()) -> false()
     app(app(le(),app(s(),x)),app(s(),y)) -> app(app(le(),x),y)
     app(app(maxlist(),x),app(app(cons(),y),ys)) ->
     app(app(if(),app(app(le(),x),y)),app(app(maxlist(),y),ys))
     app(app(maxlist(),x),nil()) -> x
     app(height(),app(app(node(),x),xs)) ->
     app(s(),app(app(maxlist(),0()),app(app(map(),height()),xs)))
    Subterm Criterion Processor:
     simple projection:
      pi(app#) = 1
     problem:
      DPs:
       
      TRS:
       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(le(),0()),y) -> true()
       app(app(le(),app(s(),x)),0()) -> false()
       app(app(le(),app(s(),x)),app(s(),y)) -> app(app(le(),x),y)
       app(app(maxlist(),x),app(app(cons(),y),ys)) ->
       app(app(if(),app(app(le(),x),y)),app(app(maxlist(),y),ys))
       app(app(maxlist(),x),nil()) -> x
       app(height(),app(app(node(),x),xs)) ->
       app(s(),app(app(maxlist(),0()),app(app(map(),height()),xs)))
     Qed
    
    DPs:
     app#(app(le(),app(s(),x)),app(s(),y)) -> app#(app(le(),x),y)
    TRS:
     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(le(),0()),y) -> true()
     app(app(le(),app(s(),x)),0()) -> false()
     app(app(le(),app(s(),x)),app(s(),y)) -> app(app(le(),x),y)
     app(app(maxlist(),x),app(app(cons(),y),ys)) ->
     app(app(if(),app(app(le(),x),y)),app(app(maxlist(),y),ys))
     app(app(maxlist(),x),nil()) -> x
     app(height(),app(app(node(),x),xs)) ->
     app(s(),app(app(maxlist(),0()),app(app(map(),height()),xs)))
    Subterm Criterion Processor:
     simple projection:
      pi(app#) = 1
     problem:
      DPs:
       
      TRS:
       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(le(),0()),y) -> true()
       app(app(le(),app(s(),x)),0()) -> false()
       app(app(le(),app(s(),x)),app(s(),y)) -> app(app(le(),x),y)
       app(app(maxlist(),x),app(app(cons(),y),ys)) ->
       app(app(if(),app(app(le(),x),y)),app(app(maxlist(),y),ys))
       app(app(maxlist(),x),nil()) -> x
       app(height(),app(app(node(),x),xs)) ->
       app(s(),app(app(maxlist(),0()),app(app(map(),height()),xs)))
     Qed