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()))))
  TDG 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()))))
   graph:
    double#() -> app#(map(),app(app(curry(),times()),app(s(),app(s(),0())))) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(cons(),app(f,x)),app(app(map(),f),xs))
    double#() -> app#(map(),app(app(curry(),times()),app(s(),app(s(),0())))) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(cons(),app(f,x))
    double#() -> app#(map(),app(app(curry(),times()),app(s(),app(s(),0())))) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x)
    double#() -> app#(map(),app(app(curry(),times()),app(s(),app(s(),0())))) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs)
    double#() -> app#(map(),app(app(curry(),times()),app(s(),app(s(),0())))) ->
    app#(app(app(curry(),g),x),y) -> app#(app(g,x),y)
    double#() -> app#(map(),app(app(curry(),times()),app(s(),app(s(),0())))) ->
    app#(app(app(curry(),g),x),y) -> app#(g,x)
    double#() -> app#(map(),app(app(curry(),times()),app(s(),app(s(),0())))) ->
    app#(app(times(),app(s(),x)),y) -> app#(app(plus(),app(app(times(),x),y)),y)
    double#() -> app#(map(),app(app(curry(),times()),app(s(),app(s(),0())))) ->
    app#(app(times(),app(s(),x)),y) -> app#(plus(),app(app(times(),x),y))
    double#() -> app#(map(),app(app(curry(),times()),app(s(),app(s(),0())))) ->
    app#(app(times(),app(s(),x)),y) -> app#(app(times(),x),y)
    double#() -> app#(map(),app(app(curry(),times()),app(s(),app(s(),0())))) ->
    app#(app(times(),app(s(),x)),y) -> app#(times(),x)
    double#() -> app#(map(),app(app(curry(),times()),app(s(),app(s(),0())))) ->
    app#(app(plus(),app(s(),x)),y) -> app#(s(),app(app(plus(),x),y))
    double#() -> app#(map(),app(app(curry(),times()),app(s(),app(s(),0())))) ->
    app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y)
    double#() -> app#(map(),app(app(curry(),times()),app(s(),app(s(),0())))) ->
    app#(app(plus(),app(s(),x)),y) -> app#(plus(),x)
    double#() -> app#(curry(),times()) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(cons(),app(f,x)),app(app(map(),f),xs))
    double#() -> app#(curry(),times()) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(cons(),app(f,x))
    double#() -> app#(curry(),times()) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x)
    double#() -> app#(curry(),times()) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs)
    double#() -> app#(curry(),times()) ->
    app#(app(app(curry(),g),x),y) -> app#(app(g,x),y)
    double#() -> app#(curry(),times()) ->
    app#(app(app(curry(),g),x),y) -> app#(g,x)
    double#() -> app#(curry(),times()) ->
    app#(app(times(),app(s(),x)),y) -> app#(app(plus(),app(app(times(),x),y)),y)
    double#() -> app#(curry(),times()) ->
    app#(app(times(),app(s(),x)),y) -> app#(plus(),app(app(times(),x),y))
    double#() -> app#(curry(),times()) ->
    app#(app(times(),app(s(),x)),y) -> app#(app(times(),x),y)
    double#() -> app#(curry(),times()) ->
    app#(app(times(),app(s(),x)),y) -> app#(times(),x)
    double#() -> app#(curry(),times()) ->
    app#(app(plus(),app(s(),x)),y) -> app#(s(),app(app(plus(),x),y))
    double#() -> app#(curry(),times()) ->
    app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y)
    double#() -> app#(curry(),times()) ->
    app#(app(plus(),app(s(),x)),y) -> app#(plus(),x)
    double#() -> app#(s(),app(s(),0())) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(cons(),app(f,x)),app(app(map(),f),xs))
    double#() -> app#(s(),app(s(),0())) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(cons(),app(f,x))
    double#() -> app#(s(),app(s(),0())) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x)
    double#() -> app#(s(),app(s(),0())) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs)
    double#() -> app#(s(),app(s(),0())) ->
    app#(app(app(curry(),g),x),y) -> app#(app(g,x),y)
    double#() -> app#(s(),app(s(),0())) ->
    app#(app(app(curry(),g),x),y) -> app#(g,x)
    double#() -> app#(s(),app(s(),0())) ->
    app#(app(times(),app(s(),x)),y) -> app#(app(plus(),app(app(times(),x),y)),y)
    double#() -> app#(s(),app(s(),0())) ->
    app#(app(times(),app(s(),x)),y) -> app#(plus(),app(app(times(),x),y))
    double#() -> app#(s(),app(s(),0())) ->
    app#(app(times(),app(s(),x)),y) -> app#(app(times(),x),y)
    double#() -> app#(s(),app(s(),0())) ->
    app#(app(times(),app(s(),x)),y) -> app#(times(),x)
    double#() -> app#(s(),app(s(),0())) ->
    app#(app(plus(),app(s(),x)),y) -> app#(s(),app(app(plus(),x),y))
    double#() -> app#(s(),app(s(),0())) ->
    app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y)
    double#() -> app#(s(),app(s(),0())) ->
    app#(app(plus(),app(s(),x)),y) -> app#(plus(),x)
    double#() -> app#(s(),0()) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(cons(),app(f,x)),app(app(map(),f),xs))
    double#() -> app#(s(),0()) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(cons(),app(f,x))
    double#() -> app#(s(),0()) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x)
    double#() -> app#(s(),0()) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs)
    double#() -> app#(s(),0()) ->
    app#(app(app(curry(),g),x),y) -> app#(app(g,x),y)
    double#() -> app#(s(),0()) ->
    app#(app(app(curry(),g),x),y) -> app#(g,x)
    double#() -> app#(s(),0()) ->
    app#(app(times(),app(s(),x)),y) -> app#(app(plus(),app(app(times(),x),y)),y)
    double#() -> app#(s(),0()) ->
    app#(app(times(),app(s(),x)),y) -> app#(plus(),app(app(times(),x),y))
    double#() -> app#(s(),0()) ->
    app#(app(times(),app(s(),x)),y) -> app#(app(times(),x),y)
    double#() -> app#(s(),0()) ->
    app#(app(times(),app(s(),x)),y) -> app#(times(),x)
    double#() -> app#(s(),0()) ->
    app#(app(plus(),app(s(),x)),y) -> app#(s(),app(app(plus(),x),y))
    double#() -> app#(s(),0()) ->
    app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y)
    double#() -> app#(s(),0()) ->
    app#(app(plus(),app(s(),x)),y) -> app#(plus(),x)
    double#() -> app#(app(curry(),times()),app(s(),app(s(),0()))) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(cons(),app(f,x)),app(app(map(),f),xs))
    double#() -> app#(app(curry(),times()),app(s(),app(s(),0()))) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(cons(),app(f,x))
    double#() -> app#(app(curry(),times()),app(s(),app(s(),0()))) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x)
    double#() -> app#(app(curry(),times()),app(s(),app(s(),0()))) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs)
    double#() -> app#(app(curry(),times()),app(s(),app(s(),0()))) ->
    app#(app(app(curry(),g),x),y) -> app#(app(g,x),y)
    double#() -> app#(app(curry(),times()),app(s(),app(s(),0()))) ->
    app#(app(app(curry(),g),x),y) -> app#(g,x)
    double#() -> app#(app(curry(),times()),app(s(),app(s(),0()))) ->
    app#(app(times(),app(s(),x)),y) -> app#(app(plus(),app(app(times(),x),y)),y)
    double#() -> app#(app(curry(),times()),app(s(),app(s(),0()))) ->
    app#(app(times(),app(s(),x)),y) -> app#(plus(),app(app(times(),x),y))
    double#() -> app#(app(curry(),times()),app(s(),app(s(),0()))) ->
    app#(app(times(),app(s(),x)),y) -> app#(app(times(),x),y)
    double#() -> app#(app(curry(),times()),app(s(),app(s(),0()))) ->
    app#(app(times(),app(s(),x)),y) -> app#(times(),x)
    double#() -> app#(app(curry(),times()),app(s(),app(s(),0()))) ->
    app#(app(plus(),app(s(),x)),y) -> app#(s(),app(app(plus(),x),y))
    double#() -> app#(app(curry(),times()),app(s(),app(s(),0()))) ->
    app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y)
    double#() -> app#(app(curry(),times()),app(s(),app(s(),0()))) ->
    app#(app(plus(),app(s(),x)),y) -> app#(plus(),x)
    inc#() -> app#(map(),app(app(curry(),plus()),app(s(),0()))) ->
    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()))) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(cons(),app(f,x))
    inc#() -> app#(map(),app(app(curry(),plus()),app(s(),0()))) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x)
    inc#() -> app#(map(),app(app(curry(),plus()),app(s(),0()))) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs)
    inc#() -> app#(map(),app(app(curry(),plus()),app(s(),0()))) ->
    app#(app(app(curry(),g),x),y) -> app#(app(g,x),y)
    inc#() -> app#(map(),app(app(curry(),plus()),app(s(),0()))) ->
    app#(app(app(curry(),g),x),y) -> app#(g,x)
    inc#() -> app#(map(),app(app(curry(),plus()),app(s(),0()))) ->
    app#(app(times(),app(s(),x)),y) -> app#(app(plus(),app(app(times(),x),y)),y)
    inc#() -> app#(map(),app(app(curry(),plus()),app(s(),0()))) ->
    app#(app(times(),app(s(),x)),y) -> app#(plus(),app(app(times(),x),y))
    inc#() -> app#(map(),app(app(curry(),plus()),app(s(),0()))) ->
    app#(app(times(),app(s(),x)),y) -> app#(app(times(),x),y)
    inc#() -> app#(map(),app(app(curry(),plus()),app(s(),0()))) ->
    app#(app(times(),app(s(),x)),y) -> app#(times(),x)
    inc#() -> app#(map(),app(app(curry(),plus()),app(s(),0()))) ->
    app#(app(plus(),app(s(),x)),y) -> app#(s(),app(app(plus(),x),y))
    inc#() -> app#(map(),app(app(curry(),plus()),app(s(),0()))) ->
    app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y)
    inc#() -> app#(map(),app(app(curry(),plus()),app(s(),0()))) ->
    app#(app(plus(),app(s(),x)),y) -> app#(plus(),x)
    inc#() -> app#(curry(),plus()) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(cons(),app(f,x)),app(app(map(),f),xs))
    inc#() -> app#(curry(),plus()) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(cons(),app(f,x))
    inc#() -> app#(curry(),plus()) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x)
    inc#() -> app#(curry(),plus()) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs)
    inc#() -> app#(curry(),plus()) ->
    app#(app(app(curry(),g),x),y) -> app#(app(g,x),y)
    inc#() -> app#(curry(),plus()) ->
    app#(app(app(curry(),g),x),y) -> app#(g,x)
    inc#() -> app#(curry(),plus()) ->
    app#(app(times(),app(s(),x)),y) -> app#(app(plus(),app(app(times(),x),y)),y)
    inc#() -> app#(curry(),plus()) ->
    app#(app(times(),app(s(),x)),y) -> app#(plus(),app(app(times(),x),y))
    inc#() -> app#(curry(),plus()) ->
    app#(app(times(),app(s(),x)),y) -> app#(app(times(),x),y)
    inc#() -> app#(curry(),plus()) ->
    app#(app(times(),app(s(),x)),y) -> app#(times(),x)
    inc#() -> app#(curry(),plus()) ->
    app#(app(plus(),app(s(),x)),y) -> app#(s(),app(app(plus(),x),y))
    inc#() -> app#(curry(),plus()) ->
    app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y)
    inc#() -> app#(curry(),plus()) ->
    app#(app(plus(),app(s(),x)),y) -> app#(plus(),x)
    inc#() -> app#(s(),0()) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(cons(),app(f,x)),app(app(map(),f),xs))
    inc#() -> app#(s(),0()) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(cons(),app(f,x))
    inc#() -> app#(s(),0()) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x)
    inc#() -> app#(s(),0()) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs)
    inc#() -> app#(s(),0()) ->
    app#(app(app(curry(),g),x),y) -> app#(app(g,x),y)
    inc#() -> app#(s(),0()) -> app#(app(app(curry(),g),x),y) -> app#(g,x)
    inc#() -> app#(s(),0()) ->
    app#(app(times(),app(s(),x)),y) -> app#(app(plus(),app(app(times(),x),y)),y)
    inc#() -> app#(s(),0()) ->
    app#(app(times(),app(s(),x)),y) -> app#(plus(),app(app(times(),x),y))
    inc#() -> app#(s(),0()) ->
    app#(app(times(),app(s(),x)),y) -> app#(app(times(),x),y)
    inc#() -> app#(s(),0()) ->
    app#(app(times(),app(s(),x)),y) -> app#(times(),x)
    inc#() -> app#(s(),0()) ->
    app#(app(plus(),app(s(),x)),y) -> app#(s(),app(app(plus(),x),y))
    inc#() -> app#(s(),0()) ->
    app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y)
    inc#() -> app#(s(),0()) ->
    app#(app(plus(),app(s(),x)),y) -> app#(plus(),x)
    inc#() -> app#(app(curry(),plus()),app(s(),0())) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(cons(),app(f,x)),app(app(map(),f),xs))
    inc#() -> app#(app(curry(),plus()),app(s(),0())) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(cons(),app(f,x))
    inc#() -> app#(app(curry(),plus()),app(s(),0())) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x)
    inc#() -> app#(app(curry(),plus()),app(s(),0())) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs)
    inc#() -> app#(app(curry(),plus()),app(s(),0())) ->
    app#(app(app(curry(),g),x),y) -> app#(app(g,x),y)
    inc#() -> app#(app(curry(),plus()),app(s(),0())) ->
    app#(app(app(curry(),g),x),y) -> app#(g,x)
    inc#() -> app#(app(curry(),plus()),app(s(),0())) ->
    app#(app(times(),app(s(),x)),y) -> app#(app(plus(),app(app(times(),x),y)),y)
    inc#() -> app#(app(curry(),plus()),app(s(),0())) ->
    app#(app(times(),app(s(),x)),y) -> app#(plus(),app(app(times(),x),y))
    inc#() -> app#(app(curry(),plus()),app(s(),0())) ->
    app#(app(times(),app(s(),x)),y) -> app#(app(times(),x),y)
    inc#() -> app#(app(curry(),plus()),app(s(),0())) ->
    app#(app(times(),app(s(),x)),y) -> app#(times(),x)
    inc#() -> app#(app(curry(),plus()),app(s(),0())) ->
    app#(app(plus(),app(s(),x)),y) -> app#(s(),app(app(plus(),x),y))
    inc#() -> app#(app(curry(),plus()),app(s(),0())) ->
    app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y)
    inc#() -> app#(app(curry(),plus()),app(s(),0())) ->
    app#(app(plus(),app(s(),x)),y) -> app#(plus(),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(map(),f),app(app(cons(),x),xs)) -> app#(cons(),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#(cons(),app(f,x)) ->
    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(map(),f),xs)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(cons(),app(f,x)) ->
    app#(app(app(curry(),g),x),y) -> app#(app(g,x),y)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(cons(),app(f,x)) ->
    app#(app(app(curry(),g),x),y) -> app#(g,x)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(cons(),app(f,x)) ->
    app#(app(times(),app(s(),x)),y) -> app#(app(plus(),app(app(times(),x),y)),y)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(cons(),app(f,x)) ->
    app#(app(times(),app(s(),x)),y) -> app#(plus(),app(app(times(),x),y))
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(cons(),app(f,x)) ->
    app#(app(times(),app(s(),x)),y) -> app#(app(times(),x),y)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(cons(),app(f,x)) ->
    app#(app(times(),app(s(),x)),y) -> app#(times(),x)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(cons(),app(f,x)) ->
    app#(app(plus(),app(s(),x)),y) -> app#(s(),app(app(plus(),x),y))
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(cons(),app(f,x)) ->
    app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(cons(),app(f,x)) ->
    app#(app(plus(),app(s(),x)),y) -> app#(plus(),x)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(cons(),app(f,x)),app(app(map(),f),xs)) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(cons(),app(f,x)),app(app(map(),f),xs))
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(cons(),app(f,x)),app(app(map(),f),xs)) ->
    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(map(),f),app(app(cons(),x),xs)) -> 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(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs)
    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)
    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(map(),f),app(app(cons(),x),xs)) -> app#(app(cons(),app(f,x)),app(app(map(),f),xs)) ->
    app#(app(times(),app(s(),x)),y) -> app#(app(plus(),app(app(times(),x),y)),y)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(cons(),app(f,x)),app(app(map(),f),xs)) ->
    app#(app(times(),app(s(),x)),y) -> app#(plus(),app(app(times(),x),y))
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(cons(),app(f,x)),app(app(map(),f),xs)) ->
    app#(app(times(),app(s(),x)),y) -> app#(app(times(),x),y)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(cons(),app(f,x)),app(app(map(),f),xs)) ->
    app#(app(times(),app(s(),x)),y) -> app#(times(),x)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(cons(),app(f,x)),app(app(map(),f),xs)) ->
    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(cons(),app(f,x)),app(app(map(),f),xs)) ->
    app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(cons(),app(f,x)),app(app(map(),f),xs)) ->
    app#(app(plus(),app(s(),x)),y) -> app#(plus(),x)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(cons(),app(f,x)),app(app(map(),f),xs))
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs) ->
    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(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#(app(map(),f),xs) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs) ->
    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(app(curry(),g),x),y) -> app#(g,x)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs) ->
    app#(app(times(),app(s(),x)),y) -> app#(app(plus(),app(app(times(),x),y)),y)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs) ->
    app#(app(times(),app(s(),x)),y) -> app#(plus(),app(app(times(),x),y))
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs) ->
    app#(app(times(),app(s(),x)),y) -> app#(app(times(),x),y)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs) ->
    app#(app(times(),app(s(),x)),y) -> app#(times(),x)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs) ->
    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(plus(),app(s(),x)),y) -> app#(app(plus(),x),y)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs) ->
    app#(app(plus(),app(s(),x)),y) -> app#(plus(),x)
    app#(app(map(),f),app(app(cons(),x),xs)) -> 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(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#(f,x) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    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(app(curry(),g),x),y) -> app#(app(g,x),y)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(app(curry(),g),x),y) -> app#(g,x)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(times(),app(s(),x)),y) -> app#(app(plus(),app(app(times(),x),y)),y)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(times(),app(s(),x)),y) -> app#(plus(),app(app(times(),x),y))
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(times(),app(s(),x)),y) -> app#(app(times(),x),y)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(times(),app(s(),x)),y) -> app#(times(),x)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(plus(),app(s(),x)),y) -> app#(s(),app(app(plus(),x),y))
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(plus(),app(s(),x)),y) -> app#(plus(),x)
    app#(app(times(),app(s(),x)),y) -> app#(times(),x) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(cons(),app(f,x)),app(app(map(),f),xs))
    app#(app(times(),app(s(),x)),y) -> app#(times(),x) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(cons(),app(f,x))
    app#(app(times(),app(s(),x)),y) -> app#(times(),x) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x)
    app#(app(times(),app(s(),x)),y) -> app#(times(),x) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs)
    app#(app(times(),app(s(),x)),y) -> app#(times(),x) ->
    app#(app(app(curry(),g),x),y) -> app#(app(g,x),y)
    app#(app(times(),app(s(),x)),y) -> app#(times(),x) ->
    app#(app(app(curry(),g),x),y) -> app#(g,x)
    app#(app(times(),app(s(),x)),y) -> app#(times(),x) ->
    app#(app(times(),app(s(),x)),y) -> app#(app(plus(),app(app(times(),x),y)),y)
    app#(app(times(),app(s(),x)),y) -> app#(times(),x) ->
    app#(app(times(),app(s(),x)),y) -> app#(plus(),app(app(times(),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#(times(),x) ->
    app#(app(times(),app(s(),x)),y) -> app#(times(),x)
    app#(app(times(),app(s(),x)),y) -> app#(times(),x) ->
    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(plus(),app(s(),x)),y) -> app#(app(plus(),x),y)
    app#(app(times(),app(s(),x)),y) -> app#(times(),x) ->
    app#(app(plus(),app(s(),x)),y) -> app#(plus(),x)
    app#(app(times(),app(s(),x)),y) -> app#(app(times(),x),y) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(cons(),app(f,x)),app(app(map(),f),xs))
    app#(app(times(),app(s(),x)),y) -> app#(app(times(),x),y) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(cons(),app(f,x))
    app#(app(times(),app(s(),x)),y) -> app#(app(times(),x),y) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x)
    app#(app(times(),app(s(),x)),y) -> app#(app(times(),x),y) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs)
    app#(app(times(),app(s(),x)),y) -> app#(app(times(),x),y) ->
    app#(app(app(curry(),g),x),y) -> app#(app(g,x),y)
    app#(app(times(),app(s(),x)),y) -> app#(app(times(),x),y) ->
    app#(app(app(curry(),g),x),y) -> app#(g,x)
    app#(app(times(),app(s(),x)),y) -> app#(app(times(),x),y) ->
    app#(app(times(),app(s(),x)),y) -> app#(app(plus(),app(app(times(),x),y)),y)
    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(times(),x),y) ->
    app#(app(times(),app(s(),x)),y) -> app#(app(times(),x),y)
    app#(app(times(),app(s(),x)),y) -> app#(app(times(),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(plus(),app(s(),x)),y) -> app#(s(),app(app(plus(),x),y))
    app#(app(times(),app(s(),x)),y) -> app#(app(times(),x),y) ->
    app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y)
    app#(app(times(),app(s(),x)),y) -> app#(app(times(),x),y) ->
    app#(app(plus(),app(s(),x)),y) -> app#(plus(),x)
    app#(app(times(),app(s(),x)),y) -> app#(app(plus(),app(app(times(),x),y)),y) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(cons(),app(f,x)),app(app(map(),f),xs))
    app#(app(times(),app(s(),x)),y) -> app#(app(plus(),app(app(times(),x),y)),y) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(cons(),app(f,x))
    app#(app(times(),app(s(),x)),y) -> app#(app(plus(),app(app(times(),x),y)),y) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x)
    app#(app(times(),app(s(),x)),y) -> app#(app(plus(),app(app(times(),x),y)),y) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs)
    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(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(times(),app(s(),x)),y) -> app#(app(plus(),app(app(times(),x),y)),y) ->
    app#(app(times(),app(s(),x)),y) -> app#(app(plus(),app(app(times(),x),y)),y)
    app#(app(times(),app(s(),x)),y) -> app#(app(plus(),app(app(times(),x),y)),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(times(),app(s(),x)),y) -> app#(app(times(),x),y)
    app#(app(times(),app(s(),x)),y) -> app#(app(plus(),app(app(times(),x),y)),y) ->
    app#(app(times(),app(s(),x)),y) -> app#(times(),x)
    app#(app(times(),app(s(),x)),y) -> app#(app(plus(),app(app(times(),x),y)),y) ->
    app#(app(plus(),app(s(),x)),y) -> app#(s(),app(app(plus(),x),y))
    app#(app(times(),app(s(),x)),y) -> app#(app(plus(),app(app(times(),x),y)),y) ->
    app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y)
    app#(app(times(),app(s(),x)),y) -> app#(app(plus(),app(app(times(),x),y)),y) ->
    app#(app(plus(),app(s(),x)),y) -> app#(plus(),x)
    app#(app(times(),app(s(),x)),y) -> app#(plus(),app(app(times(),x),y)) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(cons(),app(f,x)),app(app(map(),f),xs))
    app#(app(times(),app(s(),x)),y) -> app#(plus(),app(app(times(),x),y)) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(cons(),app(f,x))
    app#(app(times(),app(s(),x)),y) -> app#(plus(),app(app(times(),x),y)) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x)
    app#(app(times(),app(s(),x)),y) -> app#(plus(),app(app(times(),x),y)) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs)
    app#(app(times(),app(s(),x)),y) -> app#(plus(),app(app(times(),x),y)) ->
    app#(app(app(curry(),g),x),y) -> app#(app(g,x),y)
    app#(app(times(),app(s(),x)),y) -> app#(plus(),app(app(times(),x),y)) ->
    app#(app(app(curry(),g),x),y) -> app#(g,x)
    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(times(),app(s(),x)),y) -> app#(plus(),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#(plus(),app(app(times(),x),y)) ->
    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#(times(),x)
    app#(app(times(),app(s(),x)),y) -> app#(plus(),app(app(times(),x),y)) ->
    app#(app(plus(),app(s(),x)),y) -> app#(s(),app(app(plus(),x),y))
    app#(app(times(),app(s(),x)),y) -> app#(plus(),app(app(times(),x),y)) ->
    app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y)
    app#(app(times(),app(s(),x)),y) -> app#(plus(),app(app(times(),x),y)) ->
    app#(app(plus(),app(s(),x)),y) -> app#(plus(),x)
    app#(app(app(curry(),g),x),y) -> app#(app(g,x),y) ->
    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) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(cons(),app(f,x))
    app#(app(app(curry(),g),x),y) -> app#(app(g,x),y) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,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(app(curry(),g),x),y) -> app#(app(g,x),y) ->
    app#(app(app(curry(),g),x),y) -> app#(app(g,x),y)
    app#(app(app(curry(),g),x),y) -> app#(app(g,x),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(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(times(),app(s(),x)),y) -> app#(plus(),app(app(times(),x),y))
    app#(app(app(curry(),g),x),y) -> app#(app(g,x),y) ->
    app#(app(times(),app(s(),x)),y) -> app#(app(times(),x),y)
    app#(app(app(curry(),g),x),y) -> app#(app(g,x),y) ->
    app#(app(times(),app(s(),x)),y) -> app#(times(),x)
    app#(app(app(curry(),g),x),y) -> app#(app(g,x),y) ->
    app#(app(plus(),app(s(),x)),y) -> app#(s(),app(app(plus(),x),y))
    app#(app(app(curry(),g),x),y) -> app#(app(g,x),y) ->
    app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y)
    app#(app(app(curry(),g),x),y) -> app#(app(g,x),y) ->
    app#(app(plus(),app(s(),x)),y) -> app#(plus(),x)
    app#(app(app(curry(),g),x),y) -> app#(g,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(map(),f),app(app(cons(),x),xs)) -> app#(cons(),app(f,x))
    app#(app(app(curry(),g),x),y) -> app#(g,x) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x)
    app#(app(app(curry(),g),x),y) -> app#(g,x) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> 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)
    app#(app(app(curry(),g),x),y) -> app#(g,x) ->
    app#(app(app(curry(),g),x),y) -> app#(g,x)
    app#(app(app(curry(),g),x),y) -> app#(g,x) ->
    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(times(),app(s(),x)),y) -> app#(plus(),app(app(times(),x),y))
    app#(app(app(curry(),g),x),y) -> app#(g,x) ->
    app#(app(times(),app(s(),x)),y) -> app#(app(times(),x),y)
    app#(app(app(curry(),g),x),y) -> app#(g,x) ->
    app#(app(times(),app(s(),x)),y) -> app#(times(),x)
    app#(app(app(curry(),g),x),y) -> app#(g,x) ->
    app#(app(plus(),app(s(),x)),y) -> app#(s(),app(app(plus(),x),y))
    app#(app(app(curry(),g),x),y) -> app#(g,x) ->
    app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y)
    app#(app(app(curry(),g),x),y) -> app#(g,x) ->
    app#(app(plus(),app(s(),x)),y) -> app#(plus(),x)
    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(cons(),app(f,x)),app(app(map(),f),xs))
    app#(app(plus(),app(s(),x)),y) -> app#(s(),app(app(plus(),x),y)) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(cons(),app(f,x))
    app#(app(plus(),app(s(),x)),y) -> app#(s(),app(app(plus(),x),y)) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x)
    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(plus(),app(s(),x)),y) -> app#(s(),app(app(plus(),x),y)) ->
    app#(app(app(curry(),g),x),y) -> app#(app(g,x),y)
    app#(app(plus(),app(s(),x)),y) -> app#(s(),app(app(plus(),x),y)) ->
    app#(app(app(curry(),g),x),y) -> app#(g,x)
    app#(app(plus(),app(s(),x)),y) -> app#(s(),app(app(plus(),x),y)) ->
    app#(app(times(),app(s(),x)),y) -> app#(app(plus(),app(app(times(),x),y)),y)
    app#(app(plus(),app(s(),x)),y) -> app#(s(),app(app(plus(),x),y)) ->
    app#(app(times(),app(s(),x)),y) -> app#(plus(),app(app(times(),x),y))
    app#(app(plus(),app(s(),x)),y) -> app#(s(),app(app(plus(),x),y)) ->
    app#(app(times(),app(s(),x)),y) -> app#(app(times(),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(plus(),app(s(),x)),y) -> app#(s(),app(app(plus(),x),y)) ->
    app#(app(plus(),app(s(),x)),y) -> app#(s(),app(app(plus(),x),y))
    app#(app(plus(),app(s(),x)),y) -> app#(s(),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)) ->
    app#(app(plus(),app(s(),x)),y) -> app#(plus(),x)
    app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(cons(),app(f,x)),app(app(map(),f),xs))
    app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(cons(),app(f,x))
    app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x)
    app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs)
    app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y) ->
    app#(app(app(curry(),g),x),y) -> app#(app(g,x),y)
    app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y) ->
    app#(app(app(curry(),g),x),y) -> app#(g,x)
    app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y) ->
    app#(app(times(),app(s(),x)),y) -> app#(app(plus(),app(app(times(),x),y)),y)
    app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y) ->
    app#(app(times(),app(s(),x)),y) -> app#(plus(),app(app(times(),x),y))
    app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y) ->
    app#(app(times(),app(s(),x)),y) -> app#(app(times(),x),y)
    app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y) ->
    app#(app(times(),app(s(),x)),y) -> app#(times(),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(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#(plus(),x)
    app#(app(plus(),app(s(),x)),y) -> app#(plus(),x) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(cons(),app(f,x)),app(app(map(),f),xs))
    app#(app(plus(),app(s(),x)),y) -> app#(plus(),x) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(cons(),app(f,x))
    app#(app(plus(),app(s(),x)),y) -> app#(plus(),x) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x)
    app#(app(plus(),app(s(),x)),y) -> app#(plus(),x) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs)
    app#(app(plus(),app(s(),x)),y) -> app#(plus(),x) ->
    app#(app(app(curry(),g),x),y) -> app#(app(g,x),y)
    app#(app(plus(),app(s(),x)),y) -> app#(plus(),x) ->
    app#(app(app(curry(),g),x),y) -> app#(g,x)
    app#(app(plus(),app(s(),x)),y) -> app#(plus(),x) ->
    app#(app(times(),app(s(),x)),y) -> app#(app(plus(),app(app(times(),x),y)),y)
    app#(app(plus(),app(s(),x)),y) -> app#(plus(),x) ->
    app#(app(times(),app(s(),x)),y) -> app#(plus(),app(app(times(),x),y))
    app#(app(plus(),app(s(),x)),y) -> app#(plus(),x) ->
    app#(app(times(),app(s(),x)),y) -> app#(app(times(),x),y)
    app#(app(plus(),app(s(),x)),y) -> app#(plus(),x) ->
    app#(app(times(),app(s(),x)),y) -> app#(times(),x)
    app#(app(plus(),app(s(),x)),y) -> app#(plus(),x) ->
    app#(app(plus(),app(s(),x)),y) -> app#(s(),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#(plus(),x) ->
    app#(app(plus(),app(s(),x)),y) -> app#(plus(),x)
   SCC Processor:
    #sccs: 1
    #rules: 13
    #arcs: 286/484
    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))
    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()))))
    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))
      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))
     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()))))
     graph:
      app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs) ->
      app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs)
      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#(app(map(),f),xs) ->
      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(map(),f),xs) ->
      app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(cons(),app(f,x)),app(app(map(),f),xs))
      app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
      app#(app(plus(),app(s(),x)),y) -> app#(plus(),x)
      app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
      app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y)
      app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
      app#(app(plus(),app(s(),x)),y) -> app#(s(),app(app(plus(),x),y))
      app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
      app#(app(times(),app(s(),x)),y) -> app#(times(),x)
      app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
      app#(app(times(),app(s(),x)),y) -> app#(app(times(),x),y)
      app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
      app#(app(times(),app(s(),x)),y) -> app#(plus(),app(app(times(),x),y))
      app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
      app#(app(times(),app(s(),x)),y) -> app#(app(plus(),app(app(times(),x),y)),y)
      app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
      app#(app(app(curry(),g),x),y) -> app#(g,x)
      app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
      app#(app(app(curry(),g),x),y) -> app#(app(g,x),y)
      app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
      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#(f,x)
      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#(f,x) ->
      app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(cons(),app(f,x)),app(app(map(),f),xs))
      app#(app(times(),app(s(),x)),y) -> app#(app(times(),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#(app(times(),x),y)
      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(times(),x),y) ->
      app#(app(times(),app(s(),x)),y) -> app#(app(plus(),app(app(times(),x),y)),y)
      app#(app(times(),app(s(),x)),y) -> app#(app(plus(),app(app(times(),x),y)),y) ->
      app#(app(plus(),app(s(),x)),y) -> app#(plus(),x)
      app#(app(times(),app(s(),x)),y) -> app#(app(plus(),app(app(times(),x),y)),y) ->
      app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y)
      app#(app(times(),app(s(),x)),y) -> app#(app(plus(),app(app(times(),x),y)),y) ->
      app#(app(plus(),app(s(),x)),y) -> app#(s(),app(app(plus(),x),y))
      app#(app(app(curry(),g),x),y) -> app#(app(g,x),y) ->
      app#(app(plus(),app(s(),x)),y) -> app#(plus(),x)
      app#(app(app(curry(),g),x),y) -> app#(app(g,x),y) ->
      app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y)
      app#(app(app(curry(),g),x),y) -> app#(app(g,x),y) ->
      app#(app(plus(),app(s(),x)),y) -> app#(s(),app(app(plus(),x),y))
      app#(app(app(curry(),g),x),y) -> app#(app(g,x),y) ->
      app#(app(times(),app(s(),x)),y) -> app#(times(),x)
      app#(app(app(curry(),g),x),y) -> app#(app(g,x),y) ->
      app#(app(times(),app(s(),x)),y) -> app#(app(times(),x),y)
      app#(app(app(curry(),g),x),y) -> app#(app(g,x),y) ->
      app#(app(times(),app(s(),x)),y) -> app#(plus(),app(app(times(),x),y))
      app#(app(app(curry(),g),x),y) -> app#(app(g,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#(app(g,x),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(app(curry(),g),x),y) -> app#(app(g,x),y)
      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(app(curry(),g),x),y) -> app#(app(g,x),y) ->
      app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x)
      app#(app(app(curry(),g),x),y) -> app#(app(g,x),y) ->
      app#(app(map(),f),app(app(cons(),x),xs)) -> app#(cons(),app(f,x))
      app#(app(app(curry(),g),x),y) -> app#(app(g,x),y) ->
      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(plus(),app(s(),x)),y) -> app#(plus(),x)
      app#(app(app(curry(),g),x),y) -> app#(g,x) ->
      app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y)
      app#(app(app(curry(),g),x),y) -> app#(g,x) ->
      app#(app(plus(),app(s(),x)),y) -> app#(s(),app(app(plus(),x),y))
      app#(app(app(curry(),g),x),y) -> app#(g,x) ->
      app#(app(times(),app(s(),x)),y) -> app#(times(),x)
      app#(app(app(curry(),g),x),y) -> app#(g,x) ->
      app#(app(times(),app(s(),x)),y) -> app#(app(times(),x),y)
      app#(app(app(curry(),g),x),y) -> app#(g,x) ->
      app#(app(times(),app(s(),x)),y) -> app#(plus(),app(app(times(),x),y))
      app#(app(app(curry(),g),x),y) -> app#(g,x) ->
      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#(g,x)
      app#(app(app(curry(),g),x),y) -> app#(g,x) ->
      app#(app(app(curry(),g),x),y) -> app#(app(g,x),y)
      app#(app(app(curry(),g),x),y) -> app#(g,x) ->
      app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs)
      app#(app(app(curry(),g),x),y) -> app#(g,x) ->
      app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x)
      app#(app(app(curry(),g),x),y) -> app#(g,x) ->
      app#(app(map(),f),app(app(cons(),x),xs)) -> app#(cons(),app(f,x))
      app#(app(app(curry(),g),x),y) -> app#(g,x) ->
      app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(cons(),app(f,x)),app(app(map(),f),xs))
      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: 3
      #rules: 6
      #arcs: 53/169
      DPs:
       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(app(curry(),g),x),y) -> app#(app(g,x),y)
       app#(app(app(curry(),g),x),y) -> app#(g,x)
      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
      
      DPs:
       app#(app(times(),app(s(),x)),y) -> app#(app(times(),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(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
      
      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(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