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(),app(p(),app(s(),x))),app(p(),app(s(),y)))
 app(p(),app(s(),x)) -> x
 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(p1(s1(x)),p1(s1(y)))
  p1(s1(x)) -> x
  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(p(),x5) -> p1(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)) -> p{1,#}(s1(y))
    minus{2,#}(s1(x),s1(y)) -> p{1,#}(s1(x))
    minus{2,#}(s1(x),s1(y)) -> minus{2,#}(p1(s1(x)),p1(s1(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#(p(),x5) -> p{1,#}(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(p1(s1(x)),p1(s1(y)))
    p1(s1(x)) -> x
    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(p(),x5) -> p1(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)) -> p{1,#}(s1(y))
     minus{2,#}(s1(x),s1(y)) -> p{1,#}(s1(x))
     minus{2,#}(s1(x),s1(y)) -> minus{2,#}(p1(s1(x)),p1(s1(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#(p(),x5) -> p{1,#}(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(p1(s1(x)),p1(s1(y)))
     p1(s1(x)) -> x
     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(p(),x5) -> p1(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,#}(p1(s1(x)),p1(s1(y)))
     div{2,#}(s1(x),s1(y)) -> minus{2,#}(x,y) ->
     minus{2,#}(s1(x),s1(y)) -> p{1,#}(s1(x))
     div{2,#}(s1(x),s1(y)) -> minus{2,#}(x,y) ->
     minus{2,#}(s1(x),s1(y)) -> p{1,#}(s1(y))
     minus{2,#}(s1(x),s1(y)) -> minus{2,#}(p1(s1(x)),p1(s1(y))) ->
     minus{2,#}(s1(x),s1(y)) -> minus{2,#}(p1(s1(x)),p1(s1(y)))
     minus{2,#}(s1(x),s1(y)) -> minus{2,#}(p1(s1(x)),p1(s1(y))) ->
     minus{2,#}(s1(x),s1(y)) -> p{1,#}(s1(x))
     minus{2,#}(s1(x),s1(y)) -> minus{2,#}(p1(s1(x)),p1(s1(y))) ->
     minus{2,#}(s1(x),s1(y)) -> p{1,#}(s1(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,#}(p1(s1(x)),p1(s1(y)))
     app#(minus1(x4),x5) -> minus{2,#}(x4,x5) ->
     minus{2,#}(s1(x),s1(y)) -> p{1,#}(s1(x))
     app#(minus1(x4),x5) -> minus{2,#}(x4,x5) ->
     minus{2,#}(s1(x),s1(y)) -> p{1,#}(s1(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#(p(),x5) -> p{1,#}(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: 21/121
     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(p1(s1(x)),p1(s1(y)))
      p1(s1(x)) -> x
      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(p(),x5) -> p1(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(p1(s1(x)),p1(s1(y)))
        p1(s1(x)) -> x
        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(p(),x5) -> p1(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(p1(s1(x)),p1(s1(y)))
      p1(s1(x)) -> x
      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(p(),x5) -> p1(x5)
      app(div1(x4),x5) -> div2(x4,x5)
      app(div(),x5) -> div1(x5)
     Arctic Interpretation Processor:
      dimension: 1
      interpretation:
       [div{2,#}](x0, x1) = x0,
       
       [div2](x0, x1) = x0,
       
       [div1](x0) = x0,
       
       [p1](x0) = x0,
       
       [s1](x0) = 1x0 + 0,
       
       [minus2](x0, x1) = x0,
       
       [minus1](x0) = x0,
       
       [cons2](x0, x1) = x0 + 0,
       
       [cons1](x0) = x0,
       
       [map2](x0, x1) = x0 + 1x1,
       
       [map1](x0) = x0,
       
       [div] = 5,
       
       [p] = 7,
       
       [s] = 0,
       
       [0] = 2,
       
       [minus] = 2,
       
       [cons] = 3,
       
       [nil] = 4,
       
       [app](x0, x1) = x0 + 1x1 + 0,
       
       [map] = 5
      orientation:
       div{2,#}(s1(x),s1(y)) = 1x + 0 >= x = div{2,#}(minus2(x,y),s1(y))
       
       map2(f,nil()) = f + 5 >= 4 = nil()
       
       map2(f,cons2(x,xs)) = f + 1x + 1 >= f + 1x + 0 = cons2(app(f,x),map2(f,xs))
       
       minus2(x,0()) = x >= x = x
       
       minus2(s1(x),s1(y)) = 1x + 0 >= 1x + 0 = minus2(p1(s1(x)),p1(s1(y)))
       
       p1(s1(x)) = 1x + 0 >= x = x
       
       div2(0(),s1(y)) = 2 >= 2 = 0()
       
       div2(s1(x),s1(y)) = 1x + 0 >= 1x + 0 = s1(div2(minus2(x,y),s1(y)))
       
       app(map1(x4),x5) = x4 + 1x5 + 0 >= x4 + 1x5 = map2(x4,x5)
       
       app(map(),x5) = 1x5 + 5 >= x5 = map1(x5)
       
       app(cons1(x4),x5) = x4 + 1x5 + 0 >= x4 + 0 = cons2(x4,x5)
       
       app(cons(),x5) = 1x5 + 3 >= x5 = cons1(x5)
       
       app(minus1(x4),x5) = x4 + 1x5 + 0 >= x4 = minus2(x4,x5)
       
       app(minus(),x5) = 1x5 + 2 >= x5 = minus1(x5)
       
       app(s(),x5) = 1x5 + 0 >= 1x5 + 0 = s1(x5)
       
       app(p(),x5) = 1x5 + 7 >= x5 = p1(x5)
       
       app(div1(x4),x5) = x4 + 1x5 + 0 >= x4 = div2(x4,x5)
       
       app(div(),x5) = 1x5 + 5 >= x5 = 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(p1(s1(x)),p1(s1(y)))
        p1(s1(x)) -> x
        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(p(),x5) -> p1(x5)
        app(div1(x4),x5) -> div2(x4,x5)
        app(div(),x5) -> div1(x5)
      Qed
     
     DPs:
      minus{2,#}(s1(x),s1(y)) -> minus{2,#}(p1(s1(x)),p1(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(p1(s1(x)),p1(s1(y)))
      p1(s1(x)) -> x
      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(p(),x5) -> p1(x5)
      app(div1(x4),x5) -> div2(x4,x5)
      app(div(),x5) -> div1(x5)
     Matrix Interpretation Processor: dim=1
      
      interpretation:
       [minus{2,#}](x0, x1) = 1/2x0,
       
       [div2](x0, x1) = 5/2x0 + 2,
       
       [div1](x0) = 5/2x0 + 1,
       
       [p1](x0) = 1/2x0,
       
       [s1](x0) = 2x0 + 2,
       
       [minus2](x0, x1) = x0,
       
       [minus1](x0) = 2x0 + 1,
       
       [cons2](x0, x1) = 2,
       
       [cons1](x0) = 2x0 + 1,
       
       [map2](x0, x1) = 2,
       
       [map1](x0) = 1/2,
       
       [div] = 0,
       
       [p] = 2,
       
       [s] = 2,
       
       [0] = 1,
       
       [minus] = 3,
       
       [cons] = 5/2,
       
       [nil] = 0,
       
       [app](x0, x1) = x0 + 5/2x1 + 2,
       
       [map] = 7/2
      orientation:
       minus{2,#}(s1(x),s1(y)) = x + 1 >= 1/2x + 1/2 = minus{2,#}(p1(s1(x)),p1(s1(y)))
       
       map2(f,nil()) = 2 >= 0 = nil()
       
       map2(f,cons2(x,xs)) = 2 >= 2 = cons2(app(f,x),map2(f,xs))
       
       minus2(x,0()) = x >= x = x
       
       minus2(s1(x),s1(y)) = 2x + 2 >= x + 1 = minus2(p1(s1(x)),p1(s1(y)))
       
       p1(s1(x)) = x + 1 >= x = x
       
       div2(0(),s1(y)) = 9/2 >= 1 = 0()
       
       div2(s1(x),s1(y)) = 5x + 7 >= 5x + 6 = s1(div2(minus2(x,y),s1(y)))
       
       app(map1(x4),x5) = 5/2x5 + 5/2 >= 2 = map2(x4,x5)
       
       app(map(),x5) = 5/2x5 + 11/2 >= 1/2 = map1(x5)
       
       app(cons1(x4),x5) = 2x4 + 5/2x5 + 3 >= 2 = cons2(x4,x5)
       
       app(cons(),x5) = 5/2x5 + 9/2 >= 2x5 + 1 = cons1(x5)
       
       app(minus1(x4),x5) = 2x4 + 5/2x5 + 3 >= x4 = minus2(x4,x5)
       
       app(minus(),x5) = 5/2x5 + 5 >= 2x5 + 1 = minus1(x5)
       
       app(s(),x5) = 5/2x5 + 4 >= 2x5 + 2 = s1(x5)
       
       app(p(),x5) = 5/2x5 + 4 >= 1/2x5 = p1(x5)
       
       app(div1(x4),x5) = 5/2x4 + 5/2x5 + 3 >= 5/2x4 + 2 = div2(x4,x5)
       
       app(div(),x5) = 5/2x5 + 2 >= 5/2x5 + 1 = 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(p1(s1(x)),p1(s1(y)))
        p1(s1(x)) -> x
        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(p(),x5) -> p1(x5)
        app(div1(x4),x5) -> div2(x4,x5)
        app(div(),x5) -> div1(x5)
      Qed