YES

Problem:
 app(app(append(),nil()),ys) -> ys
 app(app(append(),app(app(cons(),x),xs)),ys) -> app(app(cons(),x),app(app(append(),xs),ys))
 app(app(flatwith(),f),app(leaf(),x)) -> app(app(cons(),app(f,x)),nil())
 app(app(flatwith(),f),app(node(),xs)) -> app(app(flatwithsub(),f),xs)
 app(app(flatwithsub(),f),nil()) -> nil()
 app(app(flatwithsub(),f),app(app(cons(),x),xs)) ->
 app(app(append(),app(app(flatwith(),f),x)),app(app(flatwithsub(),f),xs))

Proof:
 DP Processor:
  DPs:
   app#(app(append(),app(app(cons(),x),xs)),ys) -> app#(append(),xs)
   app#(app(append(),app(app(cons(),x),xs)),ys) -> app#(app(append(),xs),ys)
   app#(app(append(),app(app(cons(),x),xs)),ys) -> app#(app(cons(),x),app(app(append(),xs),ys))
   app#(app(flatwith(),f),app(leaf(),x)) -> app#(f,x)
   app#(app(flatwith(),f),app(leaf(),x)) -> app#(cons(),app(f,x))
   app#(app(flatwith(),f),app(leaf(),x)) -> app#(app(cons(),app(f,x)),nil())
   app#(app(flatwith(),f),app(node(),xs)) -> app#(flatwithsub(),f)
   app#(app(flatwith(),f),app(node(),xs)) -> app#(app(flatwithsub(),f),xs)
   app#(app(flatwithsub(),f),app(app(cons(),x),xs)) -> app#(app(flatwithsub(),f),xs)
   app#(app(flatwithsub(),f),app(app(cons(),x),xs)) -> app#(flatwith(),f)
   app#(app(flatwithsub(),f),app(app(cons(),x),xs)) -> app#(app(flatwith(),f),x)
   app#(app(flatwithsub(),f),app(app(cons(),x),xs)) -> app#(append(),app(app(flatwith(),f),x))
   app#(app(flatwithsub(),f),app(app(cons(),x),xs)) ->
   app#(app(append(),app(app(flatwith(),f),x)),app(app(flatwithsub(),f),xs))
  TRS:
   app(app(append(),nil()),ys) -> ys
   app(app(append(),app(app(cons(),x),xs)),ys) -> app(app(cons(),x),app(app(append(),xs),ys))
   app(app(flatwith(),f),app(leaf(),x)) -> app(app(cons(),app(f,x)),nil())
   app(app(flatwith(),f),app(node(),xs)) -> app(app(flatwithsub(),f),xs)
   app(app(flatwithsub(),f),nil()) -> nil()
   app(app(flatwithsub(),f),app(app(cons(),x),xs)) ->
   app(app(append(),app(app(flatwith(),f),x)),app(app(flatwithsub(),f),xs))
  EDG Processor:
   DPs:
    app#(app(append(),app(app(cons(),x),xs)),ys) -> app#(append(),xs)
    app#(app(append(),app(app(cons(),x),xs)),ys) -> app#(app(append(),xs),ys)
    app#(app(append(),app(app(cons(),x),xs)),ys) -> app#(app(cons(),x),app(app(append(),xs),ys))
    app#(app(flatwith(),f),app(leaf(),x)) -> app#(f,x)
    app#(app(flatwith(),f),app(leaf(),x)) -> app#(cons(),app(f,x))
    app#(app(flatwith(),f),app(leaf(),x)) -> app#(app(cons(),app(f,x)),nil())
    app#(app(flatwith(),f),app(node(),xs)) -> app#(flatwithsub(),f)
    app#(app(flatwith(),f),app(node(),xs)) -> app#(app(flatwithsub(),f),xs)
    app#(app(flatwithsub(),f),app(app(cons(),x),xs)) -> app#(app(flatwithsub(),f),xs)
    app#(app(flatwithsub(),f),app(app(cons(),x),xs)) -> app#(flatwith(),f)
    app#(app(flatwithsub(),f),app(app(cons(),x),xs)) -> app#(app(flatwith(),f),x)
    app#(app(flatwithsub(),f),app(app(cons(),x),xs)) -> app#(append(),app(app(flatwith(),f),x))
    app#(app(flatwithsub(),f),app(app(cons(),x),xs)) ->
    app#(app(append(),app(app(flatwith(),f),x)),app(app(flatwithsub(),f),xs))
   TRS:
    app(app(append(),nil()),ys) -> ys
    app(app(append(),app(app(cons(),x),xs)),ys) -> app(app(cons(),x),app(app(append(),xs),ys))
    app(app(flatwith(),f),app(leaf(),x)) -> app(app(cons(),app(f,x)),nil())
    app(app(flatwith(),f),app(node(),xs)) -> app(app(flatwithsub(),f),xs)
    app(app(flatwithsub(),f),nil()) -> nil()
    app(app(flatwithsub(),f),app(app(cons(),x),xs)) ->
    app(app(append(),app(app(flatwith(),f),x)),app(app(flatwithsub(),f),xs))
   graph:
    app#(app(flatwithsub(),f),app(app(cons(),x),xs)) -> app#(app(flatwithsub(),f),xs) ->
    app#(app(flatwithsub(),f),app(app(cons(),x),xs)) -> app#(app(flatwithsub(),f),xs)
    app#(app(flatwithsub(),f),app(app(cons(),x),xs)) -> app#(app(flatwithsub(),f),xs) ->
    app#(app(flatwithsub(),f),app(app(cons(),x),xs)) -> app#(flatwith(),f)
    app#(app(flatwithsub(),f),app(app(cons(),x),xs)) -> app#(app(flatwithsub(),f),xs) ->
    app#(app(flatwithsub(),f),app(app(cons(),x),xs)) -> app#(app(flatwith(),f),x)
    app#(app(flatwithsub(),f),app(app(cons(),x),xs)) -> app#(app(flatwithsub(),f),xs) ->
    app#(app(flatwithsub(),f),app(app(cons(),x),xs)) -> app#(append(),app(app(flatwith(),f),x))
    app#(app(flatwithsub(),f),app(app(cons(),x),xs)) -> app#(app(flatwithsub(),f),xs) ->
    app#(app(flatwithsub(),f),app(app(cons(),x),xs)) ->
    app#(app(append(),app(app(flatwith(),f),x)),app(app(flatwithsub(),f),xs))
    app#(app(flatwithsub(),f),app(app(cons(),x),xs)) -> app#(app(flatwith(),f),x) ->
    app#(app(flatwith(),f),app(leaf(),x)) -> app#(f,x)
    app#(app(flatwithsub(),f),app(app(cons(),x),xs)) -> app#(app(flatwith(),f),x) ->
    app#(app(flatwith(),f),app(leaf(),x)) -> app#(cons(),app(f,x))
    app#(app(flatwithsub(),f),app(app(cons(),x),xs)) -> app#(app(flatwith(),f),x) ->
    app#(app(flatwith(),f),app(leaf(),x)) -> app#(app(cons(),app(f,x)),nil())
    app#(app(flatwithsub(),f),app(app(cons(),x),xs)) -> app#(app(flatwith(),f),x) ->
    app#(app(flatwith(),f),app(node(),xs)) -> app#(flatwithsub(),f)
    app#(app(flatwithsub(),f),app(app(cons(),x),xs)) -> app#(app(flatwith(),f),x) ->
    app#(app(flatwith(),f),app(node(),xs)) -> app#(app(flatwithsub(),f),xs)
    app#(app(flatwithsub(),f),app(app(cons(),x),xs)) ->
    app#(app(append(),app(app(flatwith(),f),x)),app(app(flatwithsub(),f),xs)) ->
    app#(app(append(),app(app(cons(),x),xs)),ys) -> app#(append(),xs)
    app#(app(flatwithsub(),f),app(app(cons(),x),xs)) ->
    app#(app(append(),app(app(flatwith(),f),x)),app(app(flatwithsub(),f),xs)) ->
    app#(app(append(),app(app(cons(),x),xs)),ys) -> app#(app(append(),xs),ys)
    app#(app(flatwithsub(),f),app(app(cons(),x),xs)) ->
    app#(app(append(),app(app(flatwith(),f),x)),app(app(flatwithsub(),f),xs)) ->
    app#(app(append(),app(app(cons(),x),xs)),ys) -> app#(app(cons(),x),app(app(append(),xs),ys))
    app#(app(flatwith(),f),app(node(),xs)) -> app#(app(flatwithsub(),f),xs) ->
    app#(app(flatwithsub(),f),app(app(cons(),x),xs)) -> app#(app(flatwithsub(),f),xs)
    app#(app(flatwith(),f),app(node(),xs)) -> app#(app(flatwithsub(),f),xs) ->
    app#(app(flatwithsub(),f),app(app(cons(),x),xs)) -> app#(flatwith(),f)
    app#(app(flatwith(),f),app(node(),xs)) -> app#(app(flatwithsub(),f),xs) ->
    app#(app(flatwithsub(),f),app(app(cons(),x),xs)) -> app#(app(flatwith(),f),x)
    app#(app(flatwith(),f),app(node(),xs)) -> app#(app(flatwithsub(),f),xs) ->
    app#(app(flatwithsub(),f),app(app(cons(),x),xs)) -> app#(append(),app(app(flatwith(),f),x))
    app#(app(flatwith(),f),app(node(),xs)) -> app#(app(flatwithsub(),f),xs) ->
    app#(app(flatwithsub(),f),app(app(cons(),x),xs)) ->
    app#(app(append(),app(app(flatwith(),f),x)),app(app(flatwithsub(),f),xs))
    app#(app(flatwith(),f),app(leaf(),x)) -> app#(f,x) ->
    app#(app(append(),app(app(cons(),x),xs)),ys) -> app#(append(),xs)
    app#(app(flatwith(),f),app(leaf(),x)) -> app#(f,x) ->
    app#(app(append(),app(app(cons(),x),xs)),ys) -> app#(app(append(),xs),ys)
    app#(app(flatwith(),f),app(leaf(),x)) -> app#(f,x) ->
    app#(app(append(),app(app(cons(),x),xs)),ys) -> app#(app(cons(),x),app(app(append(),xs),ys))
    app#(app(flatwith(),f),app(leaf(),x)) -> app#(f,x) ->
    app#(app(flatwith(),f),app(leaf(),x)) -> app#(f,x)
    app#(app(flatwith(),f),app(leaf(),x)) -> app#(f,x) ->
    app#(app(flatwith(),f),app(leaf(),x)) -> app#(cons(),app(f,x))
    app#(app(flatwith(),f),app(leaf(),x)) -> app#(f,x) ->
    app#(app(flatwith(),f),app(leaf(),x)) -> app#(app(cons(),app(f,x)),nil())
    app#(app(flatwith(),f),app(leaf(),x)) -> app#(f,x) ->
    app#(app(flatwith(),f),app(node(),xs)) -> app#(flatwithsub(),f)
    app#(app(flatwith(),f),app(leaf(),x)) -> app#(f,x) ->
    app#(app(flatwith(),f),app(node(),xs)) -> app#(app(flatwithsub(),f),xs)
    app#(app(flatwith(),f),app(leaf(),x)) -> app#(f,x) ->
    app#(app(flatwithsub(),f),app(app(cons(),x),xs)) -> app#(app(flatwithsub(),f),xs)
    app#(app(flatwith(),f),app(leaf(),x)) -> app#(f,x) ->
    app#(app(flatwithsub(),f),app(app(cons(),x),xs)) -> app#(flatwith(),f)
    app#(app(flatwith(),f),app(leaf(),x)) -> app#(f,x) ->
    app#(app(flatwithsub(),f),app(app(cons(),x),xs)) -> app#(app(flatwith(),f),x)
    app#(app(flatwith(),f),app(leaf(),x)) -> app#(f,x) ->
    app#(app(flatwithsub(),f),app(app(cons(),x),xs)) -> app#(append(),app(app(flatwith(),f),x))
    app#(app(flatwith(),f),app(leaf(),x)) -> app#(f,x) ->
    app#(app(flatwithsub(),f),app(app(cons(),x),xs)) ->
    app#(app(append(),app(app(flatwith(),f),x)),app(app(flatwithsub(),f),xs))
    app#(app(append(),app(app(cons(),x),xs)),ys) -> app#(app(append(),xs),ys) ->
    app#(app(append(),app(app(cons(),x),xs)),ys) -> app#(append(),xs)
    app#(app(append(),app(app(cons(),x),xs)),ys) -> app#(app(append(),xs),ys) ->
    app#(app(append(),app(app(cons(),x),xs)),ys) -> app#(app(append(),xs),ys)
    app#(app(append(),app(app(cons(),x),xs)),ys) -> app#(app(append(),xs),ys) ->
    app#(app(append(),app(app(cons(),x),xs)),ys) -> app#(app(cons(),x),app(app(append(),xs),ys))
   SCC Processor:
    #sccs: 2
    #rules: 5
    #arcs: 34/169
    DPs:
     app#(app(flatwithsub(),f),app(app(cons(),x),xs)) -> app#(app(flatwithsub(),f),xs)
     app#(app(flatwithsub(),f),app(app(cons(),x),xs)) -> app#(app(flatwith(),f),x)
     app#(app(flatwith(),f),app(node(),xs)) -> app#(app(flatwithsub(),f),xs)
     app#(app(flatwith(),f),app(leaf(),x)) -> app#(f,x)
    TRS:
     app(app(append(),nil()),ys) -> ys
     app(app(append(),app(app(cons(),x),xs)),ys) -> app(app(cons(),x),app(app(append(),xs),ys))
     app(app(flatwith(),f),app(leaf(),x)) -> app(app(cons(),app(f,x)),nil())
     app(app(flatwith(),f),app(node(),xs)) -> app(app(flatwithsub(),f),xs)
     app(app(flatwithsub(),f),nil()) -> nil()
     app(app(flatwithsub(),f),app(app(cons(),x),xs)) ->
     app(app(append(),app(app(flatwith(),f),x)),app(app(flatwithsub(),f),xs))
    Subterm Criterion Processor:
     simple projection:
      pi(app#) = 1
     problem:
      DPs:
       
      TRS:
       app(app(append(),nil()),ys) -> ys
       app(app(append(),app(app(cons(),x),xs)),ys) -> app(app(cons(),x),app(app(append(),xs),ys))
       app(app(flatwith(),f),app(leaf(),x)) -> app(app(cons(),app(f,x)),nil())
       app(app(flatwith(),f),app(node(),xs)) -> app(app(flatwithsub(),f),xs)
       app(app(flatwithsub(),f),nil()) -> nil()
       app(app(flatwithsub(),f),app(app(cons(),x),xs)) ->
       app(app(append(),app(app(flatwith(),f),x)),app(app(flatwithsub(),f),xs))
     Qed
    
    DPs:
     app#(app(append(),app(app(cons(),x),xs)),ys) -> app#(app(append(),xs),ys)
    TRS:
     app(app(append(),nil()),ys) -> ys
     app(app(append(),app(app(cons(),x),xs)),ys) -> app(app(cons(),x),app(app(append(),xs),ys))
     app(app(flatwith(),f),app(leaf(),x)) -> app(app(cons(),app(f,x)),nil())
     app(app(flatwith(),f),app(node(),xs)) -> app(app(flatwithsub(),f),xs)
     app(app(flatwithsub(),f),nil()) -> nil()
     app(app(flatwithsub(),f),app(app(cons(),x),xs)) ->
     app(app(append(),app(app(flatwith(),f),x)),app(app(flatwithsub(),f),xs))
    Usable Rule Processor:
     DPs:
      app#(app(append(),app(app(cons(),x),xs)),ys) -> app#(app(append(),xs),ys)
     TRS:
      
     Bounds Processor:
      bound: 1
      enrichment: match-dp
      automaton:
       final states: {5}
       transitions:
        app{#,0}(6,4) -> 5*
        app0(3,1) -> 3*
        app0(3,3) -> 3*
        app0(1,2) -> 3*
        app0(2,1) -> 3*
        app0(2,3) -> 3*
        app0(3,2) -> 3*
        app0(1,1) -> 3*
        app0(1,3) -> 3*
        app0(2,2) -> 3*
        app0(2,4) -> 6*
        append0() -> 2*
        cons0() -> 1*
        app{#,1}(8,4) -> 5*
        app1(7,1) -> 8*
        app1(7,3) -> 8*
        app1(7,2) -> 8*
        append1() -> 7*
        1 -> 4*
        2 -> 4*
        3 -> 4*
      problem:
       DPs:
        
       TRS:
        
      Qed