YES

Problem:
 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(minus(),x),0()) -> x
 app(app(minus(),app(s(),x)),app(s(),y)) -> app(app(minus(),x),y)
 app(app(div(),0()),app(s(),y)) -> 0()
 app(app(div(),app(s(),x)),app(s(),y)) -> app(s(),app(app(div(),app(app(minus(),x),y)),app(s(),y)))

Proof:
 Uncurry Processor:
  map2(f,nil()) -> nil()
  map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
  minus2(x,0()) -> x
  minus2(s1(x),s1(y)) -> minus2(x,y)
  div2(0(),s1(y)) -> 0()
  div2(s1(x),s1(y)) -> s1(div2(minus2(x,y),s1(y)))
  app(map1(x4),x5) -> map2(x4,x5)
  app(map(),x5) -> map1(x5)
  app(cons1(x4),x5) -> cons2(x4,x5)
  app(cons(),x5) -> cons1(x5)
  app(minus1(x4),x5) -> minus2(x4,x5)
  app(minus(),x5) -> minus1(x5)
  app(s(),x5) -> s1(x5)
  app(div1(x4),x5) -> div2(x4,x5)
  app(div(),x5) -> div1(x5)
  DP Processor:
   DPs:
    map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
    map{2,#}(f,cons2(x,xs)) -> app#(f,x)
    minus{2,#}(s1(x),s1(y)) -> minus{2,#}(x,y)
    div{2,#}(s1(x),s1(y)) -> minus{2,#}(x,y)
    div{2,#}(s1(x),s1(y)) -> div{2,#}(minus2(x,y),s1(y))
    app#(map1(x4),x5) -> map{2,#}(x4,x5)
    app#(minus1(x4),x5) -> minus{2,#}(x4,x5)
    app#(div1(x4),x5) -> div{2,#}(x4,x5)
   TRS:
    map2(f,nil()) -> nil()
    map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
    minus2(x,0()) -> x
    minus2(s1(x),s1(y)) -> minus2(x,y)
    div2(0(),s1(y)) -> 0()
    div2(s1(x),s1(y)) -> s1(div2(minus2(x,y),s1(y)))
    app(map1(x4),x5) -> map2(x4,x5)
    app(map(),x5) -> map1(x5)
    app(cons1(x4),x5) -> cons2(x4,x5)
    app(cons(),x5) -> cons1(x5)
    app(minus1(x4),x5) -> minus2(x4,x5)
    app(minus(),x5) -> minus1(x5)
    app(s(),x5) -> s1(x5)
    app(div1(x4),x5) -> div2(x4,x5)
    app(div(),x5) -> div1(x5)
   TDG Processor:
    DPs:
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x)
     minus{2,#}(s1(x),s1(y)) -> minus{2,#}(x,y)
     div{2,#}(s1(x),s1(y)) -> minus{2,#}(x,y)
     div{2,#}(s1(x),s1(y)) -> div{2,#}(minus2(x,y),s1(y))
     app#(map1(x4),x5) -> map{2,#}(x4,x5)
     app#(minus1(x4),x5) -> minus{2,#}(x4,x5)
     app#(div1(x4),x5) -> div{2,#}(x4,x5)
    TRS:
     map2(f,nil()) -> nil()
     map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
     minus2(x,0()) -> x
     minus2(s1(x),s1(y)) -> minus2(x,y)
     div2(0(),s1(y)) -> 0()
     div2(s1(x),s1(y)) -> s1(div2(minus2(x,y),s1(y)))
     app(map1(x4),x5) -> map2(x4,x5)
     app(map(),x5) -> map1(x5)
     app(cons1(x4),x5) -> cons2(x4,x5)
     app(cons(),x5) -> cons1(x5)
     app(minus1(x4),x5) -> minus2(x4,x5)
     app(minus(),x5) -> minus1(x5)
     app(s(),x5) -> s1(x5)
     app(div1(x4),x5) -> div2(x4,x5)
     app(div(),x5) -> div1(x5)
    graph:
     div{2,#}(s1(x),s1(y)) -> div{2,#}(minus2(x,y),s1(y)) ->
     div{2,#}(s1(x),s1(y)) -> div{2,#}(minus2(x,y),s1(y))
     div{2,#}(s1(x),s1(y)) -> div{2,#}(minus2(x,y),s1(y)) ->
     div{2,#}(s1(x),s1(y)) -> minus{2,#}(x,y)
     div{2,#}(s1(x),s1(y)) -> minus{2,#}(x,y) ->
     minus{2,#}(s1(x),s1(y)) -> minus{2,#}(x,y)
     minus{2,#}(s1(x),s1(y)) -> minus{2,#}(x,y) ->
     minus{2,#}(s1(x),s1(y)) -> minus{2,#}(x,y)
     app#(div1(x4),x5) -> div{2,#}(x4,x5) ->
     div{2,#}(s1(x),s1(y)) -> div{2,#}(minus2(x,y),s1(y))
     app#(div1(x4),x5) -> div{2,#}(x4,x5) ->
     div{2,#}(s1(x),s1(y)) -> minus{2,#}(x,y)
     app#(minus1(x4),x5) -> minus{2,#}(x4,x5) ->
     minus{2,#}(s1(x),s1(y)) -> minus{2,#}(x,y)
     app#(map1(x4),x5) -> map{2,#}(x4,x5) ->
     map{2,#}(f,cons2(x,xs)) -> app#(f,x)
     app#(map1(x4),x5) -> map{2,#}(x4,x5) ->
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(div1(x4),x5) -> div{2,#}(x4,x5)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(minus1(x4),x5) -> minus{2,#}(x4,x5)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(map1(x4),x5) -> map{2,#}(x4,x5)
     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)
    SCC Processor:
     #sccs: 3
     #rules: 5
     #arcs: 14/64
     DPs:
      app#(map1(x4),x5) -> map{2,#}(x4,x5)
      map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
      map{2,#}(f,cons2(x,xs)) -> app#(f,x)
     TRS:
      map2(f,nil()) -> nil()
      map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
      minus2(x,0()) -> x
      minus2(s1(x),s1(y)) -> minus2(x,y)
      div2(0(),s1(y)) -> 0()
      div2(s1(x),s1(y)) -> s1(div2(minus2(x,y),s1(y)))
      app(map1(x4),x5) -> map2(x4,x5)
      app(map(),x5) -> map1(x5)
      app(cons1(x4),x5) -> cons2(x4,x5)
      app(cons(),x5) -> cons1(x5)
      app(minus1(x4),x5) -> minus2(x4,x5)
      app(minus(),x5) -> minus1(x5)
      app(s(),x5) -> s1(x5)
      app(div1(x4),x5) -> div2(x4,x5)
      app(div(),x5) -> div1(x5)
     Subterm Criterion Processor:
      simple projection:
       pi(map{2,#}) = 1
       pi(app#) = 1
      problem:
       DPs:
        app#(map1(x4),x5) -> map{2,#}(x4,x5)
       TRS:
        map2(f,nil()) -> nil()
        map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
        minus2(x,0()) -> x
        minus2(s1(x),s1(y)) -> minus2(x,y)
        div2(0(),s1(y)) -> 0()
        div2(s1(x),s1(y)) -> s1(div2(minus2(x,y),s1(y)))
        app(map1(x4),x5) -> map2(x4,x5)
        app(map(),x5) -> map1(x5)
        app(cons1(x4),x5) -> cons2(x4,x5)
        app(cons(),x5) -> cons1(x5)
        app(minus1(x4),x5) -> minus2(x4,x5)
        app(minus(),x5) -> minus1(x5)
        app(s(),x5) -> s1(x5)
        app(div1(x4),x5) -> div2(x4,x5)
        app(div(),x5) -> div1(x5)
      SCC Processor:
       #sccs: 0
       #rules: 0
       #arcs: 5/1
       
     
     DPs:
      div{2,#}(s1(x),s1(y)) -> div{2,#}(minus2(x,y),s1(y))
     TRS:
      map2(f,nil()) -> nil()
      map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
      minus2(x,0()) -> x
      minus2(s1(x),s1(y)) -> minus2(x,y)
      div2(0(),s1(y)) -> 0()
      div2(s1(x),s1(y)) -> s1(div2(minus2(x,y),s1(y)))
      app(map1(x4),x5) -> map2(x4,x5)
      app(map(),x5) -> map1(x5)
      app(cons1(x4),x5) -> cons2(x4,x5)
      app(cons(),x5) -> cons1(x5)
      app(minus1(x4),x5) -> minus2(x4,x5)
      app(minus(),x5) -> minus1(x5)
      app(s(),x5) -> s1(x5)
      app(div1(x4),x5) -> div2(x4,x5)
      app(div(),x5) -> div1(x5)
     Arctic Interpretation Processor:
      dimension: 1
      interpretation:
       [div{2,#}](x0, x1) = 2x0,
       
       [div2](x0, x1) = x0,
       
       [div1](x0) = 1x0 + 2,
       
       [s1](x0) = 1x0,
       
       [minus2](x0, x1) = x0,
       
       [minus1](x0) = x0,
       
       [cons2](x0, x1) = x1,
       
       [cons1](x0) = x0 + 2,
       
       [map2](x0, x1) = 1x0 + x1,
       
       [map1](x0) = 1x0 + 0,
       
       [div] = 4,
       
       [s] = 1,
       
       [0] = 6,
       
       [minus] = 1,
       
       [cons] = 2,
       
       [nil] = 0,
       
       [app](x0, x1) = x0 + 1x1 + 0,
       
       [map] = 0
      orientation:
       div{2,#}(s1(x),s1(y)) = 3x >= 2x = div{2,#}(minus2(x,y),s1(y))
       
       map2(f,nil()) = 1f + 0 >= 0 = nil()
       
       map2(f,cons2(x,xs)) = 1f + xs >= 1f + xs = cons2(app(f,x),map2(f,xs))
       
       minus2(x,0()) = x >= x = x
       
       minus2(s1(x),s1(y)) = 1x >= x = minus2(x,y)
       
       div2(0(),s1(y)) = 6 >= 6 = 0()
       
       div2(s1(x),s1(y)) = 1x >= 1x = s1(div2(minus2(x,y),s1(y)))
       
       app(map1(x4),x5) = 1x4 + 1x5 + 0 >= 1x4 + x5 = map2(x4,x5)
       
       app(map(),x5) = 1x5 + 0 >= 1x5 + 0 = map1(x5)
       
       app(cons1(x4),x5) = x4 + 1x5 + 2 >= x5 = cons2(x4,x5)
       
       app(cons(),x5) = 1x5 + 2 >= x5 + 2 = cons1(x5)
       
       app(minus1(x4),x5) = x4 + 1x5 + 0 >= x4 = minus2(x4,x5)
       
       app(minus(),x5) = 1x5 + 1 >= x5 = minus1(x5)
       
       app(s(),x5) = 1x5 + 1 >= 1x5 = s1(x5)
       
       app(div1(x4),x5) = 1x4 + 1x5 + 2 >= x4 = div2(x4,x5)
       
       app(div(),x5) = 1x5 + 4 >= 1x5 + 2 = div1(x5)
      problem:
       DPs:
        
       TRS:
        map2(f,nil()) -> nil()
        map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
        minus2(x,0()) -> x
        minus2(s1(x),s1(y)) -> minus2(x,y)
        div2(0(),s1(y)) -> 0()
        div2(s1(x),s1(y)) -> s1(div2(minus2(x,y),s1(y)))
        app(map1(x4),x5) -> map2(x4,x5)
        app(map(),x5) -> map1(x5)
        app(cons1(x4),x5) -> cons2(x4,x5)
        app(cons(),x5) -> cons1(x5)
        app(minus1(x4),x5) -> minus2(x4,x5)
        app(minus(),x5) -> minus1(x5)
        app(s(),x5) -> s1(x5)
        app(div1(x4),x5) -> div2(x4,x5)
        app(div(),x5) -> div1(x5)
      Qed
     
     DPs:
      minus{2,#}(s1(x),s1(y)) -> minus{2,#}(x,y)
     TRS:
      map2(f,nil()) -> nil()
      map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
      minus2(x,0()) -> x
      minus2(s1(x),s1(y)) -> minus2(x,y)
      div2(0(),s1(y)) -> 0()
      div2(s1(x),s1(y)) -> s1(div2(minus2(x,y),s1(y)))
      app(map1(x4),x5) -> map2(x4,x5)
      app(map(),x5) -> map1(x5)
      app(cons1(x4),x5) -> cons2(x4,x5)
      app(cons(),x5) -> cons1(x5)
      app(minus1(x4),x5) -> minus2(x4,x5)
      app(minus(),x5) -> minus1(x5)
      app(s(),x5) -> s1(x5)
      app(div1(x4),x5) -> div2(x4,x5)
      app(div(),x5) -> div1(x5)
     Subterm Criterion Processor:
      simple projection:
       pi(minus{2,#}) = 1
      problem:
       DPs:
        
       TRS:
        map2(f,nil()) -> nil()
        map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
        minus2(x,0()) -> x
        minus2(s1(x),s1(y)) -> minus2(x,y)
        div2(0(),s1(y)) -> 0()
        div2(s1(x),s1(y)) -> s1(div2(minus2(x,y),s1(y)))
        app(map1(x4),x5) -> map2(x4,x5)
        app(map(),x5) -> map1(x5)
        app(cons1(x4),x5) -> cons2(x4,x5)
        app(cons(),x5) -> cons1(x5)
        app(minus1(x4),x5) -> minus2(x4,x5)
        app(minus(),x5) -> minus1(x5)
        app(s(),x5) -> s1(x5)
        app(div1(x4),x5) -> div2(x4,x5)
        app(div(),x5) -> div1(x5)
      Qed