YES

Problem:
 app(id(),x) -> x
 app(plus(),0()) -> id()
 app(app(plus(),app(s(),x)),y) -> app(s(),app(app(plus(),x),y))

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))
  TRS:
   app(id(),x) -> x
   app(plus(),0()) -> id()
   app(app(plus(),app(s(),x)),y) -> app(s(),app(app(plus(),x),y))
  EDG 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))
   TRS:
    app(id(),x) -> x
    app(plus(),0()) -> id()
    app(app(plus(),app(s(),x)),y) -> app(s(),app(app(plus(),x),y))
   graph:
    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#(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#(s(),app(app(plus(),x),y))
   SCC Processor:
    #sccs: 1
    #rules: 1
    #arcs: 3/9
    DPs:
     app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y)
    TRS:
     app(id(),x) -> x
     app(plus(),0()) -> id()
     app(app(plus(),app(s(),x)),y) -> app(s(),app(app(plus(),x),y))
    Matrix Interpretation Processor:
     dimension: 1
     interpretation:
      [app#](x0, x1) = x0,
      
      [s] = 1,
      
      [0] = 0,
      
      [plus] = 0,
      
      [app](x0, x1) = x0 + x1,
      
      [id] = 0
     orientation:
      app#(app(plus(),app(s(),x)),y) = x + 1 >= x = app#(app(plus(),x),y)
      
      app(id(),x) = x >= x = x
      
      app(plus(),0()) = 0 >= 0 = id()
      
      app(app(plus(),app(s(),x)),y) = x + y + 1 >= x + y + 1 = app(s(),app(app(plus(),x),y))
     problem:
      DPs:
       
      TRS:
       app(id(),x) -> x
       app(plus(),0()) -> id()
       app(app(plus(),app(s(),x)),y) -> app(s(),app(app(plus(),x),y))
     Qed