YES

Problem:
 app(app(mapbt(),f),app(leaf(),x)) -> app(leaf(),app(f,x))
 app(app(mapbt(),f),app(app(app(branch(),x),l),r)) ->
 app(app(app(branch(),app(f,x)),app(app(mapbt(),f),l)),app(app(mapbt(),f),r))

Proof:
 Uncurry Processor:
  mapbt2(f,leaf1(x)) -> leaf1(app(f,x))
  mapbt2(f,branch3(x,l,r)) -> branch3(app(f,x),mapbt2(f,l),mapbt2(f,r))
  app(mapbt1(x5),x6) -> mapbt2(x5,x6)
  app(mapbt(),x6) -> mapbt1(x6)
  app(leaf(),x6) -> leaf1(x6)
  app(branch2(x5,x4),x6) -> branch3(x5,x4,x6)
  app(branch1(x5),x6) -> branch2(x5,x6)
  app(branch(),x6) -> branch1(x6)
  DP Processor:
   DPs:
    mapbt{2,#}(f,leaf1(x)) -> app#(f,x)
    mapbt{2,#}(f,branch3(x,l,r)) -> mapbt{2,#}(f,r)
    mapbt{2,#}(f,branch3(x,l,r)) -> mapbt{2,#}(f,l)
    mapbt{2,#}(f,branch3(x,l,r)) -> app#(f,x)
    app#(mapbt1(x5),x6) -> mapbt{2,#}(x5,x6)
   TRS:
    mapbt2(f,leaf1(x)) -> leaf1(app(f,x))
    mapbt2(f,branch3(x,l,r)) -> branch3(app(f,x),mapbt2(f,l),mapbt2(f,r))
    app(mapbt1(x5),x6) -> mapbt2(x5,x6)
    app(mapbt(),x6) -> mapbt1(x6)
    app(leaf(),x6) -> leaf1(x6)
    app(branch2(x5,x4),x6) -> branch3(x5,x4,x6)
    app(branch1(x5),x6) -> branch2(x5,x6)
    app(branch(),x6) -> branch1(x6)
   TDG Processor:
    DPs:
     mapbt{2,#}(f,leaf1(x)) -> app#(f,x)
     mapbt{2,#}(f,branch3(x,l,r)) -> mapbt{2,#}(f,r)
     mapbt{2,#}(f,branch3(x,l,r)) -> mapbt{2,#}(f,l)
     mapbt{2,#}(f,branch3(x,l,r)) -> app#(f,x)
     app#(mapbt1(x5),x6) -> mapbt{2,#}(x5,x6)
    TRS:
     mapbt2(f,leaf1(x)) -> leaf1(app(f,x))
     mapbt2(f,branch3(x,l,r)) -> branch3(app(f,x),mapbt2(f,l),mapbt2(f,r))
     app(mapbt1(x5),x6) -> mapbt2(x5,x6)
     app(mapbt(),x6) -> mapbt1(x6)
     app(leaf(),x6) -> leaf1(x6)
     app(branch2(x5,x4),x6) -> branch3(x5,x4,x6)
     app(branch1(x5),x6) -> branch2(x5,x6)
     app(branch(),x6) -> branch1(x6)
    graph:
     app#(mapbt1(x5),x6) -> mapbt{2,#}(x5,x6) ->
     mapbt{2,#}(f,branch3(x,l,r)) -> app#(f,x)
     app#(mapbt1(x5),x6) -> mapbt{2,#}(x5,x6) ->
     mapbt{2,#}(f,branch3(x,l,r)) -> mapbt{2,#}(f,l)
     app#(mapbt1(x5),x6) -> mapbt{2,#}(x5,x6) ->
     mapbt{2,#}(f,branch3(x,l,r)) -> mapbt{2,#}(f,r)
     app#(mapbt1(x5),x6) -> mapbt{2,#}(x5,x6) ->
     mapbt{2,#}(f,leaf1(x)) -> app#(f,x)
     mapbt{2,#}(f,branch3(x,l,r)) -> app#(f,x) ->
     app#(mapbt1(x5),x6) -> mapbt{2,#}(x5,x6)
     mapbt{2,#}(f,branch3(x,l,r)) -> mapbt{2,#}(f,r) ->
     mapbt{2,#}(f,branch3(x,l,r)) -> app#(f,x)
     mapbt{2,#}(f,branch3(x,l,r)) -> mapbt{2,#}(f,r) ->
     mapbt{2,#}(f,branch3(x,l,r)) -> mapbt{2,#}(f,l)
     mapbt{2,#}(f,branch3(x,l,r)) -> mapbt{2,#}(f,r) ->
     mapbt{2,#}(f,branch3(x,l,r)) -> mapbt{2,#}(f,r)
     mapbt{2,#}(f,branch3(x,l,r)) -> mapbt{2,#}(f,r) ->
     mapbt{2,#}(f,leaf1(x)) -> app#(f,x)
     mapbt{2,#}(f,branch3(x,l,r)) -> mapbt{2,#}(f,l) ->
     mapbt{2,#}(f,branch3(x,l,r)) -> app#(f,x)
     mapbt{2,#}(f,branch3(x,l,r)) -> mapbt{2,#}(f,l) ->
     mapbt{2,#}(f,branch3(x,l,r)) -> mapbt{2,#}(f,l)
     mapbt{2,#}(f,branch3(x,l,r)) -> mapbt{2,#}(f,l) ->
     mapbt{2,#}(f,branch3(x,l,r)) -> mapbt{2,#}(f,r)
     mapbt{2,#}(f,branch3(x,l,r)) -> mapbt{2,#}(f,l) ->
     mapbt{2,#}(f,leaf1(x)) -> app#(f,x)
     mapbt{2,#}(f,leaf1(x)) -> app#(f,x) -> app#(mapbt1(x5),x6) -> mapbt{2,#}(x5,x6)
    Subterm Criterion Processor:
     simple projection:
      pi(mapbt{2,#}) = 1
      pi(app#) = 1
     problem:
      DPs:
       app#(mapbt1(x5),x6) -> mapbt{2,#}(x5,x6)
      TRS:
       mapbt2(f,leaf1(x)) -> leaf1(app(f,x))
       mapbt2(f,branch3(x,l,r)) -> branch3(app(f,x),mapbt2(f,l),mapbt2(f,r))
       app(mapbt1(x5),x6) -> mapbt2(x5,x6)
       app(mapbt(),x6) -> mapbt1(x6)
       app(leaf(),x6) -> leaf1(x6)
       app(branch2(x5,x4),x6) -> branch3(x5,x4,x6)
       app(branch1(x5),x6) -> branch2(x5,x6)
       app(branch(),x6) -> branch1(x6)
     SCC Processor:
      #sccs: 0
      #rules: 0
      #arcs: 14/1