MAYBE

Problem:
 app(app(plus(),0()),y) -> y
 app(app(plus(),app(s(),x)),y) -> app(s(),app(app(plus(),x),y))
 app(app(times(),0()),y) -> 0()
 app(app(times(),app(s(),x)),y) -> app(app(plus(),app(app(times(),x),y)),y)
 app(app(app(curry(),g),x),y) -> app(app(g,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))
 inc() -> app(map(),app(app(curry(),plus()),app(s(),0())))
 double() -> app(map(),app(app(curry(),times()),app(s(),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(times(),app(s(),x)),y) -> app#(times(),x)
   app#(app(times(),app(s(),x)),y) -> app#(app(times(),x),y)
   app#(app(times(),app(s(),x)),y) -> app#(plus(),app(app(times(),x),y))
   app#(app(times(),app(s(),x)),y) -> app#(app(plus(),app(app(times(),x),y)),y)
   app#(app(app(curry(),g),x),y) -> app#(g,x)
   app#(app(app(curry(),g),x),y) -> app#(app(g,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))
   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())))
   double#() -> app#(s(),0())
   double#() -> app#(s(),app(s(),0()))
   double#() -> app#(curry(),times())
   double#() -> app#(app(curry(),times()),app(s(),app(s(),0())))
   double#() -> app#(map(),app(app(curry(),times()),app(s(),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(times(),0()),y) -> 0()
   app(app(times(),app(s(),x)),y) -> app(app(plus(),app(app(times(),x),y)),y)
   app(app(app(curry(),g),x),y) -> app(app(g,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))
   inc() -> app(map(),app(app(curry(),plus()),app(s(),0())))
   double() -> app(map(),app(app(curry(),times()),app(s(),app(s(),0()))))
  Open