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(app(comp(),f),g),x) -> app(f,app(g,x))
 app(twice(),f) -> app(app(comp(),f),f)

Proof:
 Uncurry Processor:
  map2(f,nil()) -> nil()
  map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
  comp3(f,g,x) -> app(f,app(g,x))
  twice1(f) -> comp2(f,f)
  app(map1(x5),x6) -> map2(x5,x6)
  app(map(),x6) -> map1(x6)
  app(cons1(x5),x6) -> cons2(x5,x6)
  app(cons(),x6) -> cons1(x6)
  app(comp2(x5,x4),x6) -> comp3(x5,x4,x6)
  app(comp1(x5),x6) -> comp2(x5,x6)
  app(comp(),x6) -> comp1(x6)
  app(twice(),x6) -> twice1(x6)
  DP Processor:
   DPs:
    map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
    map{2,#}(f,cons2(x,xs)) -> app#(f,x)
    comp{3,#}(f,g,x) -> app#(g,x)
    comp{3,#}(f,g,x) -> app#(f,app(g,x))
    app#(map1(x5),x6) -> map{2,#}(x5,x6)
    app#(comp2(x5,x4),x6) -> comp{3,#}(x5,x4,x6)
    app#(twice(),x6) -> twice{1,#}(x6)
   TRS:
    map2(f,nil()) -> nil()
    map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
    comp3(f,g,x) -> app(f,app(g,x))
    twice1(f) -> comp2(f,f)
    app(map1(x5),x6) -> map2(x5,x6)
    app(map(),x6) -> map1(x6)
    app(cons1(x5),x6) -> cons2(x5,x6)
    app(cons(),x6) -> cons1(x6)
    app(comp2(x5,x4),x6) -> comp3(x5,x4,x6)
    app(comp1(x5),x6) -> comp2(x5,x6)
    app(comp(),x6) -> comp1(x6)
    app(twice(),x6) -> twice1(x6)
   TDG Processor:
    DPs:
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x)
     comp{3,#}(f,g,x) -> app#(g,x)
     comp{3,#}(f,g,x) -> app#(f,app(g,x))
     app#(map1(x5),x6) -> map{2,#}(x5,x6)
     app#(comp2(x5,x4),x6) -> comp{3,#}(x5,x4,x6)
     app#(twice(),x6) -> twice{1,#}(x6)
    TRS:
     map2(f,nil()) -> nil()
     map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
     comp3(f,g,x) -> app(f,app(g,x))
     twice1(f) -> comp2(f,f)
     app(map1(x5),x6) -> map2(x5,x6)
     app(map(),x6) -> map1(x6)
     app(cons1(x5),x6) -> cons2(x5,x6)
     app(cons(),x6) -> cons1(x6)
     app(comp2(x5,x4),x6) -> comp3(x5,x4,x6)
     app(comp1(x5),x6) -> comp2(x5,x6)
     app(comp(),x6) -> comp1(x6)
     app(twice(),x6) -> twice1(x6)
    graph:
     comp{3,#}(f,g,x) -> app#(g,x) ->
     app#(twice(),x6) -> twice{1,#}(x6)
     comp{3,#}(f,g,x) -> app#(g,x) ->
     app#(comp2(x5,x4),x6) -> comp{3,#}(x5,x4,x6)
     comp{3,#}(f,g,x) -> app#(g,x) ->
     app#(map1(x5),x6) -> map{2,#}(x5,x6)
     comp{3,#}(f,g,x) -> app#(f,app(g,x)) ->
     app#(twice(),x6) -> twice{1,#}(x6)
     comp{3,#}(f,g,x) -> app#(f,app(g,x)) ->
     app#(comp2(x5,x4),x6) -> comp{3,#}(x5,x4,x6)
     comp{3,#}(f,g,x) -> app#(f,app(g,x)) ->
     app#(map1(x5),x6) -> map{2,#}(x5,x6)
     app#(comp2(x5,x4),x6) -> comp{3,#}(x5,x4,x6) ->
     comp{3,#}(f,g,x) -> app#(f,app(g,x))
     app#(comp2(x5,x4),x6) -> comp{3,#}(x5,x4,x6) ->
     comp{3,#}(f,g,x) -> app#(g,x)
     app#(map1(x5),x6) -> map{2,#}(x5,x6) ->
     map{2,#}(f,cons2(x,xs)) -> app#(f,x)
     app#(map1(x5),x6) -> map{2,#}(x5,x6) ->
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(twice(),x6) -> twice{1,#}(x6)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(comp2(x5,x4),x6) -> comp{3,#}(x5,x4,x6)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(map1(x5),x6) -> map{2,#}(x5,x6)
     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: 1
     #rules: 6
     #arcs: 15/49
     DPs:
      comp{3,#}(f,g,x) -> app#(g,x)
      app#(map1(x5),x6) -> map{2,#}(x5,x6)
      map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
      map{2,#}(f,cons2(x,xs)) -> app#(f,x)
      app#(comp2(x5,x4),x6) -> comp{3,#}(x5,x4,x6)
      comp{3,#}(f,g,x) -> app#(f,app(g,x))
     TRS:
      map2(f,nil()) -> nil()
      map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
      comp3(f,g,x) -> app(f,app(g,x))
      twice1(f) -> comp2(f,f)
      app(map1(x5),x6) -> map2(x5,x6)
      app(map(),x6) -> map1(x6)
      app(cons1(x5),x6) -> cons2(x5,x6)
      app(cons(),x6) -> cons1(x6)
      app(comp2(x5,x4),x6) -> comp3(x5,x4,x6)
      app(comp1(x5),x6) -> comp2(x5,x6)
      app(comp(),x6) -> comp1(x6)
      app(twice(),x6) -> twice1(x6)
     Size-Change Termination Processor:
      DPs:
       
      TRS:
       map2(f,nil()) -> nil()
       map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
       comp3(f,g,x) -> app(f,app(g,x))
       twice1(f) -> comp2(f,f)
       app(map1(x5),x6) -> map2(x5,x6)
       app(map(),x6) -> map1(x6)
       app(cons1(x5),x6) -> cons2(x5,x6)
       app(cons(),x6) -> cons1(x6)
       app(comp2(x5,x4),x6) -> comp3(x5,x4,x6)
       app(comp1(x5),x6) -> comp2(x5,x6)
       app(comp(),x6) -> comp1(x6)
       app(twice(),x6) -> twice1(x6)
      The DP: comp{3,#}(f,g,x) -> app#(g,x) has the edges:
        1 >=  0
        2 >=  1
      The DP: app#(map1(x5),x6) -> map{2,#}(x5,x6) has the edges:
        0 >   0
        1 >=  1
      The DP: map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs) has the edges:
        0 >=  0
        1 >   1
      The DP: map{2,#}(f,cons2(x,xs)) -> app#(f,x) has the edges:
        0 >=  0
        1 >   1
      The DP: app#(comp2(x5,x4),x6) -> comp{3,#}(x5,x4,x6) has the edges:
        0 >   1
        0 >   0
        1 >=  2
      The DP: comp{3,#}(f,g,x) -> app#(f,app(g,x)) has the edges:
        0 >=  0
      Qed