MAYBE

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)
   CDG 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:
     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#(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#(s(),app(app(plus(),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(app(curry(),f),x),y) -> app#(app(f,x),y)
     app#(app(app(curry(),f),x),y) -> app#(f,x) ->
     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#(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(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(app(curry(),f),x),y) -> app#(app(f,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#(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))
    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: 2
      #rules: 3
      #arcs: 13/36
      DPs:
       app#(app(app(curry(),f),x),y) -> app#(app(f,x),y)
       app#(app(app(curry(),f),x),y) -> app#(f,x)
      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())
      Open
      
      DPs:
       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())
      Open