YES

Problem:
 app(app(plus(),0()),y) -> y
 app(app(plus(),app(s(),x)),y) -> app(s(),app(app(plus(),x),y))
 app(app(sumwith(),f),nil()) -> nil()
 app(app(sumwith(),f),app(app(cons(),x),xs)) -> app(app(plus(),app(f,x)),app(app(sumwith(),f),xs))

Proof:
 Uncurry Processor:
  plus2(0(),y) -> y
  plus2(s1(x),y) -> s1(plus2(x,y))
  sumwith2(f,nil()) -> nil()
  sumwith2(f,cons2(x,xs)) -> plus2(app(f,x),sumwith2(f,xs))
  app(plus1(x4),x5) -> plus2(x4,x5)
  app(plus(),x5) -> plus1(x5)
  app(s(),x5) -> s1(x5)
  app(sumwith1(x4),x5) -> sumwith2(x4,x5)
  app(sumwith(),x5) -> sumwith1(x5)
  app(cons1(x4),x5) -> cons2(x4,x5)
  app(cons(),x5) -> cons1(x5)
  DP Processor:
   DPs:
    plus{2,#}(s1(x),y) -> plus{2,#}(x,y)
    sumwith{2,#}(f,cons2(x,xs)) -> sumwith{2,#}(f,xs)
    sumwith{2,#}(f,cons2(x,xs)) -> app#(f,x)
    sumwith{2,#}(f,cons2(x,xs)) -> plus{2,#}(app(f,x),sumwith2(f,xs))
    app#(plus1(x4),x5) -> plus{2,#}(x4,x5)
    app#(sumwith1(x4),x5) -> sumwith{2,#}(x4,x5)
   TRS:
    plus2(0(),y) -> y
    plus2(s1(x),y) -> s1(plus2(x,y))
    sumwith2(f,nil()) -> nil()
    sumwith2(f,cons2(x,xs)) -> plus2(app(f,x),sumwith2(f,xs))
    app(plus1(x4),x5) -> plus2(x4,x5)
    app(plus(),x5) -> plus1(x5)
    app(s(),x5) -> s1(x5)
    app(sumwith1(x4),x5) -> sumwith2(x4,x5)
    app(sumwith(),x5) -> sumwith1(x5)
    app(cons1(x4),x5) -> cons2(x4,x5)
    app(cons(),x5) -> cons1(x5)
   TDG Processor:
    DPs:
     plus{2,#}(s1(x),y) -> plus{2,#}(x,y)
     sumwith{2,#}(f,cons2(x,xs)) -> sumwith{2,#}(f,xs)
     sumwith{2,#}(f,cons2(x,xs)) -> app#(f,x)
     sumwith{2,#}(f,cons2(x,xs)) -> plus{2,#}(app(f,x),sumwith2(f,xs))
     app#(plus1(x4),x5) -> plus{2,#}(x4,x5)
     app#(sumwith1(x4),x5) -> sumwith{2,#}(x4,x5)
    TRS:
     plus2(0(),y) -> y
     plus2(s1(x),y) -> s1(plus2(x,y))
     sumwith2(f,nil()) -> nil()
     sumwith2(f,cons2(x,xs)) -> plus2(app(f,x),sumwith2(f,xs))
     app(plus1(x4),x5) -> plus2(x4,x5)
     app(plus(),x5) -> plus1(x5)
     app(s(),x5) -> s1(x5)
     app(sumwith1(x4),x5) -> sumwith2(x4,x5)
     app(sumwith(),x5) -> sumwith1(x5)
     app(cons1(x4),x5) -> cons2(x4,x5)
     app(cons(),x5) -> cons1(x5)
    graph:
     app#(sumwith1(x4),x5) -> sumwith{2,#}(x4,x5) ->
     sumwith{2,#}(f,cons2(x,xs)) -> plus{2,#}(app(f,x),sumwith2(f,xs))
     app#(sumwith1(x4),x5) -> sumwith{2,#}(x4,x5) ->
     sumwith{2,#}(f,cons2(x,xs)) -> app#(f,x)
     app#(sumwith1(x4),x5) -> sumwith{2,#}(x4,x5) ->
     sumwith{2,#}(f,cons2(x,xs)) -> sumwith{2,#}(f,xs)
     app#(plus1(x4),x5) -> plus{2,#}(x4,x5) ->
     plus{2,#}(s1(x),y) -> plus{2,#}(x,y)
     sumwith{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(sumwith1(x4),x5) -> sumwith{2,#}(x4,x5)
     sumwith{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(plus1(x4),x5) -> plus{2,#}(x4,x5)
     sumwith{2,#}(f,cons2(x,xs)) -> sumwith{2,#}(f,xs) ->
     sumwith{2,#}(f,cons2(x,xs)) -> plus{2,#}(app(f,x),sumwith2(f,xs))
     sumwith{2,#}(f,cons2(x,xs)) -> sumwith{2,#}(f,xs) ->
     sumwith{2,#}(f,cons2(x,xs)) -> app#(f,x)
     sumwith{2,#}(f,cons2(x,xs)) -> sumwith{2,#}(f,xs) ->
     sumwith{2,#}(f,cons2(x,xs)) -> sumwith{2,#}(f,xs)
     sumwith{2,#}(f,cons2(x,xs)) -> plus{2,#}(app(f,x),sumwith2(f,xs)) ->
     plus{2,#}(s1(x),y) -> plus{2,#}(x,y)
     plus{2,#}(s1(x),y) -> plus{2,#}(x,y) -> plus{2,#}(s1(x),y) -> plus{2,#}(x,y)
    SCC Processor:
     #sccs: 2
     #rules: 4
     #arcs: 11/36
     DPs:
      app#(sumwith1(x4),x5) -> sumwith{2,#}(x4,x5)
      sumwith{2,#}(f,cons2(x,xs)) -> sumwith{2,#}(f,xs)
      sumwith{2,#}(f,cons2(x,xs)) -> app#(f,x)
     TRS:
      plus2(0(),y) -> y
      plus2(s1(x),y) -> s1(plus2(x,y))
      sumwith2(f,nil()) -> nil()
      sumwith2(f,cons2(x,xs)) -> plus2(app(f,x),sumwith2(f,xs))
      app(plus1(x4),x5) -> plus2(x4,x5)
      app(plus(),x5) -> plus1(x5)
      app(s(),x5) -> s1(x5)
      app(sumwith1(x4),x5) -> sumwith2(x4,x5)
      app(sumwith(),x5) -> sumwith1(x5)
      app(cons1(x4),x5) -> cons2(x4,x5)
      app(cons(),x5) -> cons1(x5)
     Subterm Criterion Processor:
      simple projection:
       pi(sumwith{2,#}) = 1
       pi(app#) = 1
      problem:
       DPs:
        app#(sumwith1(x4),x5) -> sumwith{2,#}(x4,x5)
       TRS:
        plus2(0(),y) -> y
        plus2(s1(x),y) -> s1(plus2(x,y))
        sumwith2(f,nil()) -> nil()
        sumwith2(f,cons2(x,xs)) -> plus2(app(f,x),sumwith2(f,xs))
        app(plus1(x4),x5) -> plus2(x4,x5)
        app(plus(),x5) -> plus1(x5)
        app(s(),x5) -> s1(x5)
        app(sumwith1(x4),x5) -> sumwith2(x4,x5)
        app(sumwith(),x5) -> sumwith1(x5)
        app(cons1(x4),x5) -> cons2(x4,x5)
        app(cons(),x5) -> cons1(x5)
      SCC Processor:
       #sccs: 0
       #rules: 0
       #arcs: 5/1
       
     
     DPs:
      plus{2,#}(s1(x),y) -> plus{2,#}(x,y)
     TRS:
      plus2(0(),y) -> y
      plus2(s1(x),y) -> s1(plus2(x,y))
      sumwith2(f,nil()) -> nil()
      sumwith2(f,cons2(x,xs)) -> plus2(app(f,x),sumwith2(f,xs))
      app(plus1(x4),x5) -> plus2(x4,x5)
      app(plus(),x5) -> plus1(x5)
      app(s(),x5) -> s1(x5)
      app(sumwith1(x4),x5) -> sumwith2(x4,x5)
      app(sumwith(),x5) -> sumwith1(x5)
      app(cons1(x4),x5) -> cons2(x4,x5)
      app(cons(),x5) -> cons1(x5)
     Subterm Criterion Processor:
      simple projection:
       pi(plus{2,#}) = 0
      problem:
       DPs:
        
       TRS:
        plus2(0(),y) -> y
        plus2(s1(x),y) -> s1(plus2(x,y))
        sumwith2(f,nil()) -> nil()
        sumwith2(f,cons2(x,xs)) -> plus2(app(f,x),sumwith2(f,xs))
        app(plus1(x4),x5) -> plus2(x4,x5)
        app(plus(),x5) -> plus1(x5)
        app(s(),x5) -> s1(x5)
        app(sumwith1(x4),x5) -> sumwith2(x4,x5)
        app(sumwith(),x5) -> sumwith1(x5)
        app(cons1(x4),x5) -> cons2(x4,x5)
        app(cons(),x5) -> cons1(x5)
      Qed