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)
   Matrix Interpretation Processor: dim=1
    
    usable rules:
     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)
    interpretation:
     [add#] = 7,
     
     [app#](x0, x1) = x0,
     
     [curry] = 6,
     
     [s] = 1,
     
     [app](x0, x1) = x0 + x1,
     
     [0] = 3,
     
     [plus] = 1
    orientation:
     app#(app(plus(),app(s(),x)),y) = x + 2 >= 1 = app#(plus(),x)
     
     app#(app(plus(),app(s(),x)),y) = x + 2 >= x + 1 = app#(app(plus(),x),y)
     
     app#(app(plus(),app(s(),x)),y) = x + 2 >= 1 = app#(s(),app(app(plus(),x),y))
     
     app#(app(app(curry(),f),x),y) = f + x + 6 >= f = app#(f,x)
     
     app#(app(app(curry(),f),x),y) = f + x + 6 >= f + x = app#(app(f,x),y)
     
     add#() = 7 >= 6 = app#(curry(),plus())
     
     app(app(plus(),0()),y) = y + 4 >= y = y
     
     app(app(plus(),app(s(),x)),y) = x + y + 2 >= x + y + 2 = app(s(),app(app(plus(),x),y))
     
     app(app(app(curry(),f),x),y) = f + x + y + 6 >= f + x + y = app(app(f,x),y)
    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)
    Qed