YES

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:
 Uncurry Processor:
  plus2(0(),y) -> y
  plus2(s1(x),y) -> s1(plus2(x,y))
  times2(0(),y) -> 0()
  times2(s1(x),y) -> plus2(times2(x,y),y)
  curry3(g,x,y) -> app(app(g,x),y)
  map2(f,nil()) -> nil()
  map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
  inc() -> map1(curry2(plus(),s1(0())))
  double() -> map1(curry2(times(),s1(s1(0()))))
  app(plus1(x6),x7) -> plus2(x6,x7)
  app(plus(),x7) -> plus1(x7)
  app(s(),x7) -> s1(x7)
  app(times1(x6),x7) -> times2(x6,x7)
  app(times(),x7) -> times1(x7)
  app(curry2(x6,x5),x7) -> curry3(x6,x5,x7)
  app(curry1(x6),x7) -> curry2(x6,x7)
  app(curry(),x7) -> curry1(x7)
  app(map1(x6),x7) -> map2(x6,x7)
  app(map(),x7) -> map1(x7)
  app(cons1(x6),x7) -> cons2(x6,x7)
  app(cons(),x7) -> cons1(x7)
  DP Processor:
   DPs:
    plus{2,#}(s1(x),y) -> plus{2,#}(x,y)
    times{2,#}(s1(x),y) -> times{2,#}(x,y)
    times{2,#}(s1(x),y) -> plus{2,#}(times2(x,y),y)
    curry{3,#}(g,x,y) -> app#(g,x)
    curry{3,#}(g,x,y) -> app#(app(g,x),y)
    map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
    map{2,#}(f,cons2(x,xs)) -> app#(f,x)
    app#(plus1(x6),x7) -> plus{2,#}(x6,x7)
    app#(times1(x6),x7) -> times{2,#}(x6,x7)
    app#(curry2(x6,x5),x7) -> curry{3,#}(x6,x5,x7)
    app#(map1(x6),x7) -> map{2,#}(x6,x7)
   TRS:
    plus2(0(),y) -> y
    plus2(s1(x),y) -> s1(plus2(x,y))
    times2(0(),y) -> 0()
    times2(s1(x),y) -> plus2(times2(x,y),y)
    curry3(g,x,y) -> app(app(g,x),y)
    map2(f,nil()) -> nil()
    map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
    inc() -> map1(curry2(plus(),s1(0())))
    double() -> map1(curry2(times(),s1(s1(0()))))
    app(plus1(x6),x7) -> plus2(x6,x7)
    app(plus(),x7) -> plus1(x7)
    app(s(),x7) -> s1(x7)
    app(times1(x6),x7) -> times2(x6,x7)
    app(times(),x7) -> times1(x7)
    app(curry2(x6,x5),x7) -> curry3(x6,x5,x7)
    app(curry1(x6),x7) -> curry2(x6,x7)
    app(curry(),x7) -> curry1(x7)
    app(map1(x6),x7) -> map2(x6,x7)
    app(map(),x7) -> map1(x7)
    app(cons1(x6),x7) -> cons2(x6,x7)
    app(cons(),x7) -> cons1(x7)
   TDG Processor:
    DPs:
     plus{2,#}(s1(x),y) -> plus{2,#}(x,y)
     times{2,#}(s1(x),y) -> times{2,#}(x,y)
     times{2,#}(s1(x),y) -> plus{2,#}(times2(x,y),y)
     curry{3,#}(g,x,y) -> app#(g,x)
     curry{3,#}(g,x,y) -> app#(app(g,x),y)
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x)
     app#(plus1(x6),x7) -> plus{2,#}(x6,x7)
     app#(times1(x6),x7) -> times{2,#}(x6,x7)
     app#(curry2(x6,x5),x7) -> curry{3,#}(x6,x5,x7)
     app#(map1(x6),x7) -> map{2,#}(x6,x7)
    TRS:
     plus2(0(),y) -> y
     plus2(s1(x),y) -> s1(plus2(x,y))
     times2(0(),y) -> 0()
     times2(s1(x),y) -> plus2(times2(x,y),y)
     curry3(g,x,y) -> app(app(g,x),y)
     map2(f,nil()) -> nil()
     map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
     inc() -> map1(curry2(plus(),s1(0())))
     double() -> map1(curry2(times(),s1(s1(0()))))
     app(plus1(x6),x7) -> plus2(x6,x7)
     app(plus(),x7) -> plus1(x7)
     app(s(),x7) -> s1(x7)
     app(times1(x6),x7) -> times2(x6,x7)
     app(times(),x7) -> times1(x7)
     app(curry2(x6,x5),x7) -> curry3(x6,x5,x7)
     app(curry1(x6),x7) -> curry2(x6,x7)
     app(curry(),x7) -> curry1(x7)
     app(map1(x6),x7) -> map2(x6,x7)
     app(map(),x7) -> map1(x7)
     app(cons1(x6),x7) -> cons2(x6,x7)
     app(cons(),x7) -> cons1(x7)
    graph:
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs) ->
     map{2,#}(f,cons2(x,xs)) -> app#(f,x)
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs) ->
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(map1(x6),x7) -> map{2,#}(x6,x7)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(curry2(x6,x5),x7) -> curry{3,#}(x6,x5,x7)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(times1(x6),x7) -> times{2,#}(x6,x7)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(plus1(x6),x7) -> plus{2,#}(x6,x7)
     app#(map1(x6),x7) -> map{2,#}(x6,x7) ->
     map{2,#}(f,cons2(x,xs)) -> app#(f,x)
     app#(map1(x6),x7) -> map{2,#}(x6,x7) ->
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
     app#(curry2(x6,x5),x7) -> curry{3,#}(x6,x5,x7) ->
     curry{3,#}(g,x,y) -> app#(app(g,x),y)
     app#(curry2(x6,x5),x7) -> curry{3,#}(x6,x5,x7) ->
     curry{3,#}(g,x,y) -> app#(g,x)
     app#(times1(x6),x7) -> times{2,#}(x6,x7) ->
     times{2,#}(s1(x),y) -> plus{2,#}(times2(x,y),y)
     app#(times1(x6),x7) -> times{2,#}(x6,x7) ->
     times{2,#}(s1(x),y) -> times{2,#}(x,y)
     app#(plus1(x6),x7) -> plus{2,#}(x6,x7) ->
     plus{2,#}(s1(x),y) -> plus{2,#}(x,y)
     curry{3,#}(g,x,y) -> app#(app(g,x),y) ->
     app#(map1(x6),x7) -> map{2,#}(x6,x7)
     curry{3,#}(g,x,y) -> app#(app(g,x),y) ->
     app#(curry2(x6,x5),x7) -> curry{3,#}(x6,x5,x7)
     curry{3,#}(g,x,y) -> app#(app(g,x),y) ->
     app#(times1(x6),x7) -> times{2,#}(x6,x7)
     curry{3,#}(g,x,y) -> app#(app(g,x),y) ->
     app#(plus1(x6),x7) -> plus{2,#}(x6,x7)
     curry{3,#}(g,x,y) -> app#(g,x) ->
     app#(map1(x6),x7) -> map{2,#}(x6,x7)
     curry{3,#}(g,x,y) -> app#(g,x) ->
     app#(curry2(x6,x5),x7) -> curry{3,#}(x6,x5,x7)
     curry{3,#}(g,x,y) -> app#(g,x) ->
     app#(times1(x6),x7) -> times{2,#}(x6,x7)
     curry{3,#}(g,x,y) -> app#(g,x) ->
     app#(plus1(x6),x7) -> plus{2,#}(x6,x7)
     times{2,#}(s1(x),y) -> times{2,#}(x,y) ->
     times{2,#}(s1(x),y) -> plus{2,#}(times2(x,y),y)
     times{2,#}(s1(x),y) -> times{2,#}(x,y) ->
     times{2,#}(s1(x),y) -> times{2,#}(x,y)
     times{2,#}(s1(x),y) -> plus{2,#}(times2(x,y),y) ->
     plus{2,#}(s1(x),y) -> plus{2,#}(x,y)
     plus{2,#}(s1(x),y) -> plus{2,#}(x,y) -> plus{2,#}(s1(x),y) -> plus{2,#}(x,y)
    SCC Processor:
     #sccs: 3
     #rules: 8
     #arcs: 25/121
     DPs:
      map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
      map{2,#}(f,cons2(x,xs)) -> app#(f,x)
      app#(curry2(x6,x5),x7) -> curry{3,#}(x6,x5,x7)
      curry{3,#}(g,x,y) -> app#(g,x)
      app#(map1(x6),x7) -> map{2,#}(x6,x7)
      curry{3,#}(g,x,y) -> app#(app(g,x),y)
     TRS:
      plus2(0(),y) -> y
      plus2(s1(x),y) -> s1(plus2(x,y))
      times2(0(),y) -> 0()
      times2(s1(x),y) -> plus2(times2(x,y),y)
      curry3(g,x,y) -> app(app(g,x),y)
      map2(f,nil()) -> nil()
      map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
      inc() -> map1(curry2(plus(),s1(0())))
      double() -> map1(curry2(times(),s1(s1(0()))))
      app(plus1(x6),x7) -> plus2(x6,x7)
      app(plus(),x7) -> plus1(x7)
      app(s(),x7) -> s1(x7)
      app(times1(x6),x7) -> times2(x6,x7)
      app(times(),x7) -> times1(x7)
      app(curry2(x6,x5),x7) -> curry3(x6,x5,x7)
      app(curry1(x6),x7) -> curry2(x6,x7)
      app(curry(),x7) -> curry1(x7)
      app(map1(x6),x7) -> map2(x6,x7)
      app(map(),x7) -> map1(x7)
      app(cons1(x6),x7) -> cons2(x6,x7)
      app(cons(),x7) -> cons1(x7)
     Arctic Interpretation Processor:
      dimension: 1
      interpretation:
       [map{2,#}](x0, x1) = x0 + 0,
       
       [app#](x0, x1) = x0,
       
       [curry{3,#}](x0, x1, x2) = 1x0 + x1,
       
       [cons2](x0, x1) = x1,
       
       [cons1](x0) = x0,
       
       [map2](x0, x1) = x0 + x1,
       
       [map1](x0) = x0 + 0,
       
       [curry1](x0) = x0 + 3,
       
       [curry3](x0, x1, x2) = 2x0 + 1x1 + x2,
       
       [curry2](x0, x1) = 1x0 + x1 + 0,
       
       [times2](x0, x1) = 1x0 + x1 + 2,
       
       [times1](x0) = x0 + 1,
       
       [s1](x0) = x0,
       
       [plus2](x0, x1) = x1,
       
       [plus1](x0) = 1,
       
       [double] = 1,
       
       [inc] = 3,
       
       [cons] = 3,
       
       [nil] = 2,
       
       [map] = 4,
       
       [curry] = 6,
       
       [times] = 0,
       
       [s] = 4,
       
       [app](x0, x1) = 1x0 + x1,
       
       [0] = 0,
       
       [plus] = 1
      orientation:
       map{2,#}(f,cons2(x,xs)) = f + 0 >= f + 0 = map{2,#}(f,xs)
       
       map{2,#}(f,cons2(x,xs)) = f + 0 >= f = app#(f,x)
       
       app#(curry2(x6,x5),x7) = x5 + 1x6 + 0 >= x5 + 1x6 = curry{3,#}(x6,x5,x7)
       
       curry{3,#}(g,x,y) = 1g + x >= g = app#(g,x)
       
       app#(map1(x6),x7) = x6 + 0 >= x6 + 0 = map{2,#}(x6,x7)
       
       curry{3,#}(g,x,y) = 1g + x >= 1g + x = app#(app(g,x),y)
       
       plus2(0(),y) = y >= y = y
       
       plus2(s1(x),y) = y >= y = s1(plus2(x,y))
       
       times2(0(),y) = y + 2 >= 0 = 0()
       
       times2(s1(x),y) = 1x + y + 2 >= y = plus2(times2(x,y),y)
       
       curry3(g,x,y) = 2g + 1x + y >= 2g + 1x + y = app(app(g,x),y)
       
       map2(f,nil()) = f + 2 >= 2 = nil()
       
       map2(f,cons2(x,xs)) = f + xs >= f + xs = cons2(app(f,x),map2(f,xs))
       
       inc() = 3 >= 2 = map1(curry2(plus(),s1(0())))
       
       double() = 1 >= 1 = map1(curry2(times(),s1(s1(0()))))
       
       app(plus1(x6),x7) = x7 + 2 >= x7 = plus2(x6,x7)
       
       app(plus(),x7) = x7 + 2 >= 1 = plus1(x7)
       
       app(s(),x7) = x7 + 5 >= x7 = s1(x7)
       
       app(times1(x6),x7) = 1x6 + x7 + 2 >= 1x6 + x7 + 2 = times2(x6,x7)
       
       app(times(),x7) = x7 + 1 >= x7 + 1 = times1(x7)
       
       app(curry2(x6,x5),x7) = 1x5 + 2x6 + x7 + 1 >= 1x5 + 2x6 + x7 = curry3(x6,x5,x7)
       
       app(curry1(x6),x7) = 1x6 + x7 + 4 >= 1x6 + x7 + 0 = curry2(x6,x7)
       
       app(curry(),x7) = x7 + 7 >= x7 + 3 = curry1(x7)
       
       app(map1(x6),x7) = 1x6 + x7 + 1 >= x6 + x7 = map2(x6,x7)
       
       app(map(),x7) = x7 + 5 >= x7 + 0 = map1(x7)
       
       app(cons1(x6),x7) = 1x6 + x7 >= x7 = cons2(x6,x7)
       
       app(cons(),x7) = x7 + 4 >= x7 = cons1(x7)
      problem:
       DPs:
        map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
        map{2,#}(f,cons2(x,xs)) -> app#(f,x)
        app#(curry2(x6,x5),x7) -> curry{3,#}(x6,x5,x7)
        app#(map1(x6),x7) -> map{2,#}(x6,x7)
        curry{3,#}(g,x,y) -> app#(app(g,x),y)
       TRS:
        plus2(0(),y) -> y
        plus2(s1(x),y) -> s1(plus2(x,y))
        times2(0(),y) -> 0()
        times2(s1(x),y) -> plus2(times2(x,y),y)
        curry3(g,x,y) -> app(app(g,x),y)
        map2(f,nil()) -> nil()
        map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
        inc() -> map1(curry2(plus(),s1(0())))
        double() -> map1(curry2(times(),s1(s1(0()))))
        app(plus1(x6),x7) -> plus2(x6,x7)
        app(plus(),x7) -> plus1(x7)
        app(s(),x7) -> s1(x7)
        app(times1(x6),x7) -> times2(x6,x7)
        app(times(),x7) -> times1(x7)
        app(curry2(x6,x5),x7) -> curry3(x6,x5,x7)
        app(curry1(x6),x7) -> curry2(x6,x7)
        app(curry(),x7) -> curry1(x7)
        app(map1(x6),x7) -> map2(x6,x7)
        app(map(),x7) -> map1(x7)
        app(cons1(x6),x7) -> cons2(x6,x7)
        app(cons(),x7) -> cons1(x7)
      Subterm Criterion Processor:
       simple projection:
        pi(curry{3,#}) = 2
        pi(app#) = 1
        pi(map{2,#}) = 1
       problem:
        DPs:
         app#(curry2(x6,x5),x7) -> curry{3,#}(x6,x5,x7)
         app#(map1(x6),x7) -> map{2,#}(x6,x7)
         curry{3,#}(g,x,y) -> app#(app(g,x),y)
        TRS:
         plus2(0(),y) -> y
         plus2(s1(x),y) -> s1(plus2(x,y))
         times2(0(),y) -> 0()
         times2(s1(x),y) -> plus2(times2(x,y),y)
         curry3(g,x,y) -> app(app(g,x),y)
         map2(f,nil()) -> nil()
         map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
         inc() -> map1(curry2(plus(),s1(0())))
         double() -> map1(curry2(times(),s1(s1(0()))))
         app(plus1(x6),x7) -> plus2(x6,x7)
         app(plus(),x7) -> plus1(x7)
         app(s(),x7) -> s1(x7)
         app(times1(x6),x7) -> times2(x6,x7)
         app(times(),x7) -> times1(x7)
         app(curry2(x6,x5),x7) -> curry3(x6,x5,x7)
         app(curry1(x6),x7) -> curry2(x6,x7)
         app(curry(),x7) -> curry1(x7)
         app(map1(x6),x7) -> map2(x6,x7)
         app(map(),x7) -> map1(x7)
         app(cons1(x6),x7) -> cons2(x6,x7)
         app(cons(),x7) -> cons1(x7)
       SCC Processor:
        #sccs: 1
        #rules: 2
        #arcs: 12/9
        DPs:
         app#(curry2(x6,x5),x7) -> curry{3,#}(x6,x5,x7)
         curry{3,#}(g,x,y) -> app#(app(g,x),y)
        TRS:
         plus2(0(),y) -> y
         plus2(s1(x),y) -> s1(plus2(x,y))
         times2(0(),y) -> 0()
         times2(s1(x),y) -> plus2(times2(x,y),y)
         curry3(g,x,y) -> app(app(g,x),y)
         map2(f,nil()) -> nil()
         map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
         inc() -> map1(curry2(plus(),s1(0())))
         double() -> map1(curry2(times(),s1(s1(0()))))
         app(plus1(x6),x7) -> plus2(x6,x7)
         app(plus(),x7) -> plus1(x7)
         app(s(),x7) -> s1(x7)
         app(times1(x6),x7) -> times2(x6,x7)
         app(times(),x7) -> times1(x7)
         app(curry2(x6,x5),x7) -> curry3(x6,x5,x7)
         app(curry1(x6),x7) -> curry2(x6,x7)
         app(curry(),x7) -> curry1(x7)
         app(map1(x6),x7) -> map2(x6,x7)
         app(map(),x7) -> map1(x7)
         app(cons1(x6),x7) -> cons2(x6,x7)
         app(cons(),x7) -> cons1(x7)
        Matrix Interpretation Processor: dim=1
         
         interpretation:
          [app#](x0, x1) = 2x0,
          
          [curry{3,#}](x0, x1, x2) = 4x0 + 2x1,
          
          [cons2](x0, x1) = 0,
          
          [cons1](x0) = 4,
          
          [map2](x0, x1) = 0,
          
          [map1](x0) = 0,
          
          [curry1](x0) = x0 + 2,
          
          [curry3](x0, x1, x2) = 4x0 + 2x1 + x2 + 4,
          
          [curry2](x0, x1) = 2x0 + x1 + 4,
          
          [times2](x0, x1) = 2x0 + x1 + 1,
          
          [times1](x0) = x0 + 1,
          
          [s1](x0) = 0,
          
          [plus2](x0, x1) = x1 + 1,
          
          [plus1](x0) = 4,
          
          [double] = 0,
          
          [inc] = 1,
          
          [cons] = 3,
          
          [nil] = 0,
          
          [map] = 4,
          
          [curry] = 4,
          
          [times] = 7,
          
          [s] = 4,
          
          [app](x0, x1) = 2x0 + x1,
          
          [0] = 2,
          
          [plus] = 4
         orientation:
          app#(curry2(x6,x5),x7) = 2x5 + 4x6 + 8 >= 2x5 + 4x6 = curry{3,#}(x6,x5,x7)
          
          curry{3,#}(g,x,y) = 4g + 2x >= 4g + 2x = app#(app(g,x),y)
          
          plus2(0(),y) = y + 1 >= y = y
          
          plus2(s1(x),y) = y + 1 >= 0 = s1(plus2(x,y))
          
          times2(0(),y) = y + 5 >= 2 = 0()
          
          times2(s1(x),y) = y + 1 >= y + 1 = plus2(times2(x,y),y)
          
          curry3(g,x,y) = 4g + 2x + y + 4 >= 4g + 2x + y = app(app(g,x),y)
          
          map2(f,nil()) = 0 >= 0 = nil()
          
          map2(f,cons2(x,xs)) = 0 >= 0 = cons2(app(f,x),map2(f,xs))
          
          inc() = 1 >= 0 = map1(curry2(plus(),s1(0())))
          
          double() = 0 >= 0 = map1(curry2(times(),s1(s1(0()))))
          
          app(plus1(x6),x7) = x7 + 8 >= x7 + 1 = plus2(x6,x7)
          
          app(plus(),x7) = x7 + 8 >= 4 = plus1(x7)
          
          app(s(),x7) = x7 + 8 >= 0 = s1(x7)
          
          app(times1(x6),x7) = 2x6 + x7 + 2 >= 2x6 + x7 + 1 = times2(x6,x7)
          
          app(times(),x7) = x7 + 14 >= x7 + 1 = times1(x7)
          
          app(curry2(x6,x5),x7) = 2x5 + 4x6 + x7 + 8 >= 2x5 + 4x6 + x7 + 4 = curry3(x6,x5,x7)
          
          app(curry1(x6),x7) = 2x6 + x7 + 4 >= 2x6 + x7 + 4 = curry2(x6,x7)
          
          app(curry(),x7) = x7 + 8 >= x7 + 2 = curry1(x7)
          
          app(map1(x6),x7) = x7 >= 0 = map2(x6,x7)
          
          app(map(),x7) = x7 + 8 >= 0 = map1(x7)
          
          app(cons1(x6),x7) = x7 + 8 >= 0 = cons2(x6,x7)
          
          app(cons(),x7) = x7 + 6 >= 4 = cons1(x7)
         problem:
          DPs:
           curry{3,#}(g,x,y) -> app#(app(g,x),y)
          TRS:
           plus2(0(),y) -> y
           plus2(s1(x),y) -> s1(plus2(x,y))
           times2(0(),y) -> 0()
           times2(s1(x),y) -> plus2(times2(x,y),y)
           curry3(g,x,y) -> app(app(g,x),y)
           map2(f,nil()) -> nil()
           map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
           inc() -> map1(curry2(plus(),s1(0())))
           double() -> map1(curry2(times(),s1(s1(0()))))
           app(plus1(x6),x7) -> plus2(x6,x7)
           app(plus(),x7) -> plus1(x7)
           app(s(),x7) -> s1(x7)
           app(times1(x6),x7) -> times2(x6,x7)
           app(times(),x7) -> times1(x7)
           app(curry2(x6,x5),x7) -> curry3(x6,x5,x7)
           app(curry1(x6),x7) -> curry2(x6,x7)
           app(curry(),x7) -> curry1(x7)
           app(map1(x6),x7) -> map2(x6,x7)
           app(map(),x7) -> map1(x7)
           app(cons1(x6),x7) -> cons2(x6,x7)
           app(cons(),x7) -> cons1(x7)
         SCC Processor:
          #sccs: 0
          #rules: 0
          #arcs: 2/1
          
     
     DPs:
      times{2,#}(s1(x),y) -> times{2,#}(x,y)
     TRS:
      plus2(0(),y) -> y
      plus2(s1(x),y) -> s1(plus2(x,y))
      times2(0(),y) -> 0()
      times2(s1(x),y) -> plus2(times2(x,y),y)
      curry3(g,x,y) -> app(app(g,x),y)
      map2(f,nil()) -> nil()
      map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
      inc() -> map1(curry2(plus(),s1(0())))
      double() -> map1(curry2(times(),s1(s1(0()))))
      app(plus1(x6),x7) -> plus2(x6,x7)
      app(plus(),x7) -> plus1(x7)
      app(s(),x7) -> s1(x7)
      app(times1(x6),x7) -> times2(x6,x7)
      app(times(),x7) -> times1(x7)
      app(curry2(x6,x5),x7) -> curry3(x6,x5,x7)
      app(curry1(x6),x7) -> curry2(x6,x7)
      app(curry(),x7) -> curry1(x7)
      app(map1(x6),x7) -> map2(x6,x7)
      app(map(),x7) -> map1(x7)
      app(cons1(x6),x7) -> cons2(x6,x7)
      app(cons(),x7) -> cons1(x7)
     Subterm Criterion Processor:
      simple projection:
       pi(times{2,#}) = 0
      problem:
       DPs:
        
       TRS:
        plus2(0(),y) -> y
        plus2(s1(x),y) -> s1(plus2(x,y))
        times2(0(),y) -> 0()
        times2(s1(x),y) -> plus2(times2(x,y),y)
        curry3(g,x,y) -> app(app(g,x),y)
        map2(f,nil()) -> nil()
        map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
        inc() -> map1(curry2(plus(),s1(0())))
        double() -> map1(curry2(times(),s1(s1(0()))))
        app(plus1(x6),x7) -> plus2(x6,x7)
        app(plus(),x7) -> plus1(x7)
        app(s(),x7) -> s1(x7)
        app(times1(x6),x7) -> times2(x6,x7)
        app(times(),x7) -> times1(x7)
        app(curry2(x6,x5),x7) -> curry3(x6,x5,x7)
        app(curry1(x6),x7) -> curry2(x6,x7)
        app(curry(),x7) -> curry1(x7)
        app(map1(x6),x7) -> map2(x6,x7)
        app(map(),x7) -> map1(x7)
        app(cons1(x6),x7) -> cons2(x6,x7)
        app(cons(),x7) -> cons1(x7)
      Qed
     
     DPs:
      plus{2,#}(s1(x),y) -> plus{2,#}(x,y)
     TRS:
      plus2(0(),y) -> y
      plus2(s1(x),y) -> s1(plus2(x,y))
      times2(0(),y) -> 0()
      times2(s1(x),y) -> plus2(times2(x,y),y)
      curry3(g,x,y) -> app(app(g,x),y)
      map2(f,nil()) -> nil()
      map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
      inc() -> map1(curry2(plus(),s1(0())))
      double() -> map1(curry2(times(),s1(s1(0()))))
      app(plus1(x6),x7) -> plus2(x6,x7)
      app(plus(),x7) -> plus1(x7)
      app(s(),x7) -> s1(x7)
      app(times1(x6),x7) -> times2(x6,x7)
      app(times(),x7) -> times1(x7)
      app(curry2(x6,x5),x7) -> curry3(x6,x5,x7)
      app(curry1(x6),x7) -> curry2(x6,x7)
      app(curry(),x7) -> curry1(x7)
      app(map1(x6),x7) -> map2(x6,x7)
      app(map(),x7) -> map1(x7)
      app(cons1(x6),x7) -> cons2(x6,x7)
      app(cons(),x7) -> cons1(x7)
     Subterm Criterion Processor:
      simple projection:
       pi(plus{2,#}) = 0
      problem:
       DPs:
        
       TRS:
        plus2(0(),y) -> y
        plus2(s1(x),y) -> s1(plus2(x,y))
        times2(0(),y) -> 0()
        times2(s1(x),y) -> plus2(times2(x,y),y)
        curry3(g,x,y) -> app(app(g,x),y)
        map2(f,nil()) -> nil()
        map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
        inc() -> map1(curry2(plus(),s1(0())))
        double() -> map1(curry2(times(),s1(s1(0()))))
        app(plus1(x6),x7) -> plus2(x6,x7)
        app(plus(),x7) -> plus1(x7)
        app(s(),x7) -> s1(x7)
        app(times1(x6),x7) -> times2(x6,x7)
        app(times(),x7) -> times1(x7)
        app(curry2(x6,x5),x7) -> curry3(x6,x5,x7)
        app(curry1(x6),x7) -> curry2(x6,x7)
        app(curry(),x7) -> curry1(x7)
        app(map1(x6),x7) -> map2(x6,x7)
        app(map(),x7) -> map1(x7)
        app(cons1(x6),x7) -> cons2(x6,x7)
        app(cons(),x7) -> cons1(x7)
      Qed