YES

Problem:
 app(app(plus(),0()),y) -> y
 app(app(plus(),app(s(),x)),y) -> app(s(),app(app(plus(),x),y))
 app(app(app(curry(),f),x),y) -> app(app(f,x),y)
 add() -> app(curry(),plus())

Proof:
 DP Processor:
  DPs:
   app#(app(plus(),app(s(),x)),y) -> app#(plus(),x)
   app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y)
   app#(app(plus(),app(s(),x)),y) -> app#(s(),app(app(plus(),x),y))
   app#(app(app(curry(),f),x),y) -> app#(f,x)
   app#(app(app(curry(),f),x),y) -> app#(app(f,x),y)
   add#() -> app#(curry(),plus())
  TRS:
   app(app(plus(),0()),y) -> y
   app(app(plus(),app(s(),x)),y) -> app(s(),app(app(plus(),x),y))
   app(app(app(curry(),f),x),y) -> app(app(f,x),y)
   add() -> app(curry(),plus())
  Usable Rule Processor:
   DPs:
    app#(app(plus(),app(s(),x)),y) -> app#(plus(),x)
    app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y)
    app#(app(plus(),app(s(),x)),y) -> app#(s(),app(app(plus(),x),y))
    app#(app(app(curry(),f),x),y) -> app#(f,x)
    app#(app(app(curry(),f),x),y) -> app#(app(f,x),y)
    add#() -> app#(curry(),plus())
   TRS:
    app(app(plus(),0()),y) -> y
    app(app(plus(),app(s(),x)),y) -> app(s(),app(app(plus(),x),y))
    app(app(app(curry(),f),x),y) -> app(app(f,x),y)
   TDG Processor:
    DPs:
     app#(app(plus(),app(s(),x)),y) -> app#(plus(),x)
     app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y)
     app#(app(plus(),app(s(),x)),y) -> app#(s(),app(app(plus(),x),y))
     app#(app(app(curry(),f),x),y) -> app#(f,x)
     app#(app(app(curry(),f),x),y) -> app#(app(f,x),y)
     add#() -> app#(curry(),plus())
    TRS:
     app(app(plus(),0()),y) -> y
     app(app(plus(),app(s(),x)),y) -> app(s(),app(app(plus(),x),y))
     app(app(app(curry(),f),x),y) -> app(app(f,x),y)
    graph:
     add#() -> app#(curry(),plus()) ->
     app#(app(app(curry(),f),x),y) -> app#(app(f,x),y)
     add#() -> app#(curry(),plus()) ->
     app#(app(app(curry(),f),x),y) -> app#(f,x)
     add#() -> app#(curry(),plus()) ->
     app#(app(plus(),app(s(),x)),y) -> app#(s(),app(app(plus(),x),y))
     add#() -> app#(curry(),plus()) ->
     app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y)
     add#() -> app#(curry(),plus()) ->
     app#(app(plus(),app(s(),x)),y) -> app#(plus(),x)
     app#(app(app(curry(),f),x),y) -> app#(app(f,x),y) ->
     app#(app(app(curry(),f),x),y) -> app#(app(f,x),y)
     app#(app(app(curry(),f),x),y) -> app#(app(f,x),y) ->
     app#(app(app(curry(),f),x),y) -> app#(f,x)
     app#(app(app(curry(),f),x),y) -> app#(app(f,x),y) ->
     app#(app(plus(),app(s(),x)),y) -> app#(s(),app(app(plus(),x),y))
     app#(app(app(curry(),f),x),y) -> app#(app(f,x),y) ->
     app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y)
     app#(app(app(curry(),f),x),y) -> app#(app(f,x),y) ->
     app#(app(plus(),app(s(),x)),y) -> app#(plus(),x)
     app#(app(app(curry(),f),x),y) -> app#(f,x) ->
     app#(app(app(curry(),f),x),y) -> app#(app(f,x),y)
     app#(app(app(curry(),f),x),y) -> app#(f,x) ->
     app#(app(app(curry(),f),x),y) -> app#(f,x)
     app#(app(app(curry(),f),x),y) -> app#(f,x) ->
     app#(app(plus(),app(s(),x)),y) -> app#(s(),app(app(plus(),x),y))
     app#(app(app(curry(),f),x),y) -> app#(f,x) ->
     app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y)
     app#(app(app(curry(),f),x),y) -> app#(f,x) ->
     app#(app(plus(),app(s(),x)),y) -> app#(plus(),x)
     app#(app(plus(),app(s(),x)),y) -> app#(s(),app(app(plus(),x),y)) ->
     app#(app(app(curry(),f),x),y) -> app#(app(f,x),y)
     app#(app(plus(),app(s(),x)),y) -> app#(s(),app(app(plus(),x),y)) ->
     app#(app(app(curry(),f),x),y) -> app#(f,x)
     app#(app(plus(),app(s(),x)),y) -> app#(s(),app(app(plus(),x),y)) ->
     app#(app(plus(),app(s(),x)),y) -> app#(s(),app(app(plus(),x),y))
     app#(app(plus(),app(s(),x)),y) -> app#(s(),app(app(plus(),x),y)) ->
     app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y)
     app#(app(plus(),app(s(),x)),y) -> app#(s(),app(app(plus(),x),y)) ->
     app#(app(plus(),app(s(),x)),y) -> app#(plus(),x)
     app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y) ->
     app#(app(app(curry(),f),x),y) -> app#(app(f,x),y)
     app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y) ->
     app#(app(app(curry(),f),x),y) -> app#(f,x)
     app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y) ->
     app#(app(plus(),app(s(),x)),y) -> app#(s(),app(app(plus(),x),y))
     app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y) ->
     app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y)
     app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y) ->
     app#(app(plus(),app(s(),x)),y) -> app#(plus(),x)
     app#(app(plus(),app(s(),x)),y) -> app#(plus(),x) ->
     app#(app(app(curry(),f),x),y) -> app#(app(f,x),y)
     app#(app(plus(),app(s(),x)),y) -> app#(plus(),x) ->
     app#(app(app(curry(),f),x),y) -> app#(f,x)
     app#(app(plus(),app(s(),x)),y) -> app#(plus(),x) ->
     app#(app(plus(),app(s(),x)),y) -> app#(s(),app(app(plus(),x),y))
     app#(app(plus(),app(s(),x)),y) -> app#(plus(),x) ->
     app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y)
     app#(app(plus(),app(s(),x)),y) -> app#(plus(),x) ->
     app#(app(plus(),app(s(),x)),y) -> app#(plus(),x)
    Restore Modifier:
     DPs:
      app#(app(plus(),app(s(),x)),y) -> app#(plus(),x)
      app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y)
      app#(app(plus(),app(s(),x)),y) -> app#(s(),app(app(plus(),x),y))
      app#(app(app(curry(),f),x),y) -> app#(f,x)
      app#(app(app(curry(),f),x),y) -> app#(app(f,x),y)
      add#() -> app#(curry(),plus())
     TRS:
      app(app(plus(),0()),y) -> y
      app(app(plus(),app(s(),x)),y) -> app(s(),app(app(plus(),x),y))
      app(app(app(curry(),f),x),y) -> app(app(f,x),y)
      add() -> app(curry(),plus())
     SCC Processor:
      #sccs: 1
      #rules: 5
      #arcs: 30/36
      DPs:
       app#(app(plus(),app(s(),x)),y) -> app#(plus(),x)
       app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y)
       app#(app(plus(),app(s(),x)),y) -> app#(s(),app(app(plus(),x),y))
       app#(app(app(curry(),f),x),y) -> app#(f,x)
       app#(app(app(curry(),f),x),y) -> app#(app(f,x),y)
      TRS:
       app(app(plus(),0()),y) -> y
       app(app(plus(),app(s(),x)),y) -> app(s(),app(app(plus(),x),y))
       app(app(app(curry(),f),x),y) -> app(app(f,x),y)
       add() -> app(curry(),plus())
      Matrix Interpretation Processor:
       dimension: 1
       interpretation:
        [app#](x0, x1) = x0 + x1,
        
        [add] = 1,
        
        [curry] = 1,
        
        [s] = 0,
        
        [app](x0, x1) = x0 + x1,
        
        [0] = 0,
        
        [plus] = 0
       orientation:
        app#(app(plus(),app(s(),x)),y) = x + y >= x = app#(plus(),x)
        
        app#(app(plus(),app(s(),x)),y) = x + y >= x + y = app#(app(plus(),x),y)
        
        app#(app(plus(),app(s(),x)),y) = x + y >= x + y = app#(s(),app(app(plus(),x),y))
        
        app#(app(app(curry(),f),x),y) = f + x + y + 1 >= f + x = app#(f,x)
        
        app#(app(app(curry(),f),x),y) = f + x + y + 1 >= f + x + y = app#(app(f,x),y)
        
        app(app(plus(),0()),y) = y >= y = y
        
        app(app(plus(),app(s(),x)),y) = x + y >= x + y = app(s(),app(app(plus(),x),y))
        
        app(app(app(curry(),f),x),y) = f + x + y + 1 >= f + x + y = app(app(f,x),y)
        
        add() = 1 >= 1 = app(curry(),plus())
       problem:
        DPs:
         app#(app(plus(),app(s(),x)),y) -> app#(plus(),x)
         app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y)
         app#(app(plus(),app(s(),x)),y) -> app#(s(),app(app(plus(),x),y))
        TRS:
         app(app(plus(),0()),y) -> y
         app(app(plus(),app(s(),x)),y) -> app(s(),app(app(plus(),x),y))
         app(app(app(curry(),f),x),y) -> app(app(f,x),y)
         add() -> app(curry(),plus())
       Matrix Interpretation Processor:
        dimension: 1
        interpretation:
         [app#](x0, x1) = x0,
         
         [add] = 1,
         
         [curry] = 0,
         
         [s] = 0,
         
         [app](x0, x1) = x0 + x1,
         
         [0] = 0,
         
         [plus] = 1
        orientation:
         app#(app(plus(),app(s(),x)),y) = x + 1 >= 1 = app#(plus(),x)
         
         app#(app(plus(),app(s(),x)),y) = x + 1 >= x + 1 = app#(app(plus(),x),y)
         
         app#(app(plus(),app(s(),x)),y) = x + 1 >= 0 = app#(s(),app(app(plus(),x),y))
         
         app(app(plus(),0()),y) = y + 1 >= y = y
         
         app(app(plus(),app(s(),x)),y) = x + y + 1 >= x + y + 1 = app(s(),app(app(plus(),x),y))
         
         app(app(app(curry(),f),x),y) = f + x + y >= f + x + y = app(app(f,x),y)
         
         add() = 1 >= 1 = app(curry(),plus())
        problem:
         DPs:
          app#(app(plus(),app(s(),x)),y) -> app#(plus(),x)
          app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y)
         TRS:
          app(app(plus(),0()),y) -> y
          app(app(plus(),app(s(),x)),y) -> app(s(),app(app(plus(),x),y))
          app(app(app(curry(),f),x),y) -> app(app(f,x),y)
          add() -> app(curry(),plus())
        Matrix Interpretation Processor:
         dimension: 1
         interpretation:
          [app#](x0, x1) = x0 + x1,
          
          [add] = 1,
          
          [curry] = 0,
          
          [s] = 1,
          
          [app](x0, x1) = x0 + x1,
          
          [0] = 0,
          
          [plus] = 0
         orientation:
          app#(app(plus(),app(s(),x)),y) = x + y + 1 >= x = app#(plus(),x)
          
          app#(app(plus(),app(s(),x)),y) = x + y + 1 >= x + y = app#(app(plus(),x),y)
          
          app(app(plus(),0()),y) = y >= y = y
          
          app(app(plus(),app(s(),x)),y) = x + y + 1 >= x + y + 1 = app(s(),app(app(plus(),x),y))
          
          app(app(app(curry(),f),x),y) = f + x + y >= f + x + y = app(app(f,x),y)
          
          add() = 1 >= 0 = app(curry(),plus())
         problem:
          DPs:
           
          TRS:
           app(app(plus(),0()),y) -> y
           app(app(plus(),app(s(),x)),y) -> app(s(),app(app(plus(),x),y))
           app(app(app(curry(),f),x),y) -> app(app(f,x),y)
           add() -> app(curry(),plus())
         Qed