MAYBE

Problem:
 app(app(plus(),0()),y) -> y
 app(app(plus(),app(s(),x)),y) -> app(s(),app(app(plus(),x),y))
 app(app(map(),f),nil()) -> nil()
 app(app(map(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(f,x)),app(app(map(),f),xs))
 app(app(app(curry(),g),x),y) -> app(app(g,x),y)
 inc() -> app(map(),app(app(curry(),plus()),app(s(),0())))

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(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs)
   app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x)
   app#(app(map(),f),app(app(cons(),x),xs)) -> app#(cons(),app(f,x))
   app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(cons(),app(f,x)),app(app(map(),f),xs))
   app#(app(app(curry(),g),x),y) -> app#(g,x)
   app#(app(app(curry(),g),x),y) -> app#(app(g,x),y)
   inc#() -> app#(s(),0())
   inc#() -> app#(curry(),plus())
   inc#() -> app#(app(curry(),plus()),app(s(),0()))
   inc#() -> app#(map(),app(app(curry(),plus()),app(s(),0())))
  TRS:
   app(app(plus(),0()),y) -> y
   app(app(plus(),app(s(),x)),y) -> app(s(),app(app(plus(),x),y))
   app(app(map(),f),nil()) -> nil()
   app(app(map(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(f,x)),app(app(map(),f),xs))
   app(app(app(curry(),g),x),y) -> app(app(g,x),y)
   inc() -> app(map(),app(app(curry(),plus()),app(s(),0())))
  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(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(cons(),app(f,x))
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(cons(),app(f,x)),app(app(map(),f),xs))
    app#(app(app(curry(),g),x),y) -> app#(g,x)
    app#(app(app(curry(),g),x),y) -> app#(app(g,x),y)
    inc#() -> app#(s(),0())
    inc#() -> app#(curry(),plus())
    inc#() -> app#(app(curry(),plus()),app(s(),0()))
    inc#() -> app#(map(),app(app(curry(),plus()),app(s(),0())))
   TRS:
    app(app(plus(),0()),y) -> y
    app(app(plus(),app(s(),x)),y) -> app(s(),app(app(plus(),x),y))
    app(app(map(),f),nil()) -> nil()
    app(app(map(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(f,x)),app(app(map(),f),xs))
    app(app(app(curry(),g),x),y) -> app(app(g,x),y)
   Open