YES

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

Proof:
 Uncurry Processor:
  comp3(f,g,x) -> app(f,app(g,x))
  twice1(f) -> comp2(f,f)
  app(comp2(x4,x3),x5) -> comp3(x4,x3,x5)
  app(comp1(x4),x5) -> comp2(x4,x5)
  app(comp(),x5) -> comp1(x5)
  app(twice(),x5) -> twice1(x5)
  DP Processor:
   DPs:
    comp{3,#}(f,g,x) -> app#(g,x)
    comp{3,#}(f,g,x) -> app#(f,app(g,x))
    app#(comp2(x4,x3),x5) -> comp{3,#}(x4,x3,x5)
    app#(twice(),x5) -> twice{1,#}(x5)
   TRS:
    comp3(f,g,x) -> app(f,app(g,x))
    twice1(f) -> comp2(f,f)
    app(comp2(x4,x3),x5) -> comp3(x4,x3,x5)
    app(comp1(x4),x5) -> comp2(x4,x5)
    app(comp(),x5) -> comp1(x5)
    app(twice(),x5) -> twice1(x5)
   TDG Processor:
    DPs:
     comp{3,#}(f,g,x) -> app#(g,x)
     comp{3,#}(f,g,x) -> app#(f,app(g,x))
     app#(comp2(x4,x3),x5) -> comp{3,#}(x4,x3,x5)
     app#(twice(),x5) -> twice{1,#}(x5)
    TRS:
     comp3(f,g,x) -> app(f,app(g,x))
     twice1(f) -> comp2(f,f)
     app(comp2(x4,x3),x5) -> comp3(x4,x3,x5)
     app(comp1(x4),x5) -> comp2(x4,x5)
     app(comp(),x5) -> comp1(x5)
     app(twice(),x5) -> twice1(x5)
    graph:
     app#(comp2(x4,x3),x5) -> comp{3,#}(x4,x3,x5) ->
     comp{3,#}(f,g,x) -> app#(f,app(g,x))
     app#(comp2(x4,x3),x5) -> comp{3,#}(x4,x3,x5) ->
     comp{3,#}(f,g,x) -> app#(g,x)
     comp{3,#}(f,g,x) -> app#(g,x) ->
     app#(twice(),x5) -> twice{1,#}(x5)
     comp{3,#}(f,g,x) -> app#(g,x) ->
     app#(comp2(x4,x3),x5) -> comp{3,#}(x4,x3,x5)
     comp{3,#}(f,g,x) -> app#(f,app(g,x)) ->
     app#(twice(),x5) -> twice{1,#}(x5)
     comp{3,#}(f,g,x) -> app#(f,app(g,x)) -> app#(comp2(x4,x3),x5) -> comp{3,#}(x4,x3,x5)
    SCC Processor:
     #sccs: 1
     #rules: 3
     #arcs: 6/16
     DPs:
      app#(comp2(x4,x3),x5) -> comp{3,#}(x4,x3,x5)
      comp{3,#}(f,g,x) -> app#(g,x)
      comp{3,#}(f,g,x) -> app#(f,app(g,x))
     TRS:
      comp3(f,g,x) -> app(f,app(g,x))
      twice1(f) -> comp2(f,f)
      app(comp2(x4,x3),x5) -> comp3(x4,x3,x5)
      app(comp1(x4),x5) -> comp2(x4,x5)
      app(comp(),x5) -> comp1(x5)
      app(twice(),x5) -> twice1(x5)
     Size-Change Termination Processor:
      DPs:
       
      TRS:
       comp3(f,g,x) -> app(f,app(g,x))
       twice1(f) -> comp2(f,f)
       app(comp2(x4,x3),x5) -> comp3(x4,x3,x5)
       app(comp1(x4),x5) -> comp2(x4,x5)
       app(comp(),x5) -> comp1(x5)
       app(twice(),x5) -> twice1(x5)
      The DP: app#(comp2(x4,x3),x5) -> comp{3,#}(x4,x3,x5) has the edges:
        0 >   1
        0 >   0
        1 >=  2
      The DP: comp{3,#}(f,g,x) -> app#(g,x) has the edges:
        1 >=  0
        2 >=  1
      The DP: comp{3,#}(f,g,x) -> app#(f,app(g,x)) has the edges:
        0 >=  0
      Qed