YES

Problem:
 app(app(plus(),0()),y) -> y
 app(app(plus(),app(s(),x)),y) -> app(s(),app(app(plus(),x),y))
 app(app(times(),0()),y) -> 0()
 app(app(times(),app(s(),x)),y) -> app(app(plus(),app(app(times(),x),y)),y)
 app(app(app(comp(),f),g),x) -> app(f,app(g,x))
 app(twice(),f) -> app(app(comp(),f),f)

Proof:
 Uncurry Processor:
  plus2(0(),y) -> y
  plus2(s1(x),y) -> s1(plus2(x,y))
  times2(0(),y) -> 0()
  times2(s1(x),y) -> plus2(times2(x,y),y)
  comp3(f,g,x) -> app(f,app(g,x))
  twice1(f) -> comp2(f,f)
  app(plus1(x5),x6) -> plus2(x5,x6)
  app(plus(),x6) -> plus1(x6)
  app(s(),x6) -> s1(x6)
  app(times1(x5),x6) -> times2(x5,x6)
  app(times(),x6) -> times1(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:
    plus{2,#}(s1(x),y) -> plus{2,#}(x,y)
    times{2,#}(s1(x),y) -> times{2,#}(x,y)
    times{2,#}(s1(x),y) -> plus{2,#}(times2(x,y),y)
    comp{3,#}(f,g,x) -> app#(g,x)
    comp{3,#}(f,g,x) -> app#(f,app(g,x))
    app#(plus1(x5),x6) -> plus{2,#}(x5,x6)
    app#(times1(x5),x6) -> times{2,#}(x5,x6)
    app#(comp2(x5,x4),x6) -> comp{3,#}(x5,x4,x6)
    app#(twice(),x6) -> twice{1,#}(x6)
   TRS:
    plus2(0(),y) -> y
    plus2(s1(x),y) -> s1(plus2(x,y))
    times2(0(),y) -> 0()
    times2(s1(x),y) -> plus2(times2(x,y),y)
    comp3(f,g,x) -> app(f,app(g,x))
    twice1(f) -> comp2(f,f)
    app(plus1(x5),x6) -> plus2(x5,x6)
    app(plus(),x6) -> plus1(x6)
    app(s(),x6) -> s1(x6)
    app(times1(x5),x6) -> times2(x5,x6)
    app(times(),x6) -> times1(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:
     plus{2,#}(s1(x),y) -> plus{2,#}(x,y)
     times{2,#}(s1(x),y) -> times{2,#}(x,y)
     times{2,#}(s1(x),y) -> plus{2,#}(times2(x,y),y)
     comp{3,#}(f,g,x) -> app#(g,x)
     comp{3,#}(f,g,x) -> app#(f,app(g,x))
     app#(plus1(x5),x6) -> plus{2,#}(x5,x6)
     app#(times1(x5),x6) -> times{2,#}(x5,x6)
     app#(comp2(x5,x4),x6) -> comp{3,#}(x5,x4,x6)
     app#(twice(),x6) -> twice{1,#}(x6)
    TRS:
     plus2(0(),y) -> y
     plus2(s1(x),y) -> s1(plus2(x,y))
     times2(0(),y) -> 0()
     times2(s1(x),y) -> plus2(times2(x,y),y)
     comp3(f,g,x) -> app(f,app(g,x))
     twice1(f) -> comp2(f,f)
     app(plus1(x5),x6) -> plus2(x5,x6)
     app(plus(),x6) -> plus1(x6)
     app(s(),x6) -> s1(x6)
     app(times1(x5),x6) -> times2(x5,x6)
     app(times(),x6) -> times1(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:
     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#(times1(x5),x6) -> times{2,#}(x5,x6) ->
     times{2,#}(s1(x),y) -> plus{2,#}(times2(x,y),y)
     app#(times1(x5),x6) -> times{2,#}(x5,x6) ->
     times{2,#}(s1(x),y) -> times{2,#}(x,y)
     app#(plus1(x5),x6) -> plus{2,#}(x5,x6) ->
     plus{2,#}(s1(x),y) -> plus{2,#}(x,y)
     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#(times1(x5),x6) -> times{2,#}(x5,x6)
     comp{3,#}(f,g,x) -> app#(g,x) ->
     app#(plus1(x5),x6) -> plus{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#(times1(x5),x6) -> times{2,#}(x5,x6)
     comp{3,#}(f,g,x) -> app#(f,app(g,x)) ->
     app#(plus1(x5),x6) -> plus{2,#}(x5,x6)
     times{2,#}(s1(x),y) -> times{2,#}(x,y) ->
     times{2,#}(s1(x),y) -> plus{2,#}(times2(x,y),y)
     times{2,#}(s1(x),y) -> times{2,#}(x,y) ->
     times{2,#}(s1(x),y) -> times{2,#}(x,y)
     times{2,#}(s1(x),y) -> plus{2,#}(times2(x,y),y) ->
     plus{2,#}(s1(x),y) -> plus{2,#}(x,y)
     plus{2,#}(s1(x),y) -> plus{2,#}(x,y) -> plus{2,#}(s1(x),y) -> plus{2,#}(x,y)
    SCC Processor:
     #sccs: 3
     #rules: 5
     #arcs: 17/81
     DPs:
      app#(comp2(x5,x4),x6) -> comp{3,#}(x5,x4,x6)
      comp{3,#}(f,g,x) -> app#(g,x)
      comp{3,#}(f,g,x) -> app#(f,app(g,x))
     TRS:
      plus2(0(),y) -> y
      plus2(s1(x),y) -> s1(plus2(x,y))
      times2(0(),y) -> 0()
      times2(s1(x),y) -> plus2(times2(x,y),y)
      comp3(f,g,x) -> app(f,app(g,x))
      twice1(f) -> comp2(f,f)
      app(plus1(x5),x6) -> plus2(x5,x6)
      app(plus(),x6) -> plus1(x6)
      app(s(),x6) -> s1(x6)
      app(times1(x5),x6) -> times2(x5,x6)
      app(times(),x6) -> times1(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:
       plus2(0(),y) -> y
       plus2(s1(x),y) -> s1(plus2(x,y))
       times2(0(),y) -> 0()
       times2(s1(x),y) -> plus2(times2(x,y),y)
       comp3(f,g,x) -> app(f,app(g,x))
       twice1(f) -> comp2(f,f)
       app(plus1(x5),x6) -> plus2(x5,x6)
       app(plus(),x6) -> plus1(x6)
       app(s(),x6) -> s1(x6)
       app(times1(x5),x6) -> times2(x5,x6)
       app(times(),x6) -> times1(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: 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#(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
     
     DPs:
      times{2,#}(s1(x),y) -> times{2,#}(x,y)
     TRS:
      plus2(0(),y) -> y
      plus2(s1(x),y) -> s1(plus2(x,y))
      times2(0(),y) -> 0()
      times2(s1(x),y) -> plus2(times2(x,y),y)
      comp3(f,g,x) -> app(f,app(g,x))
      twice1(f) -> comp2(f,f)
      app(plus1(x5),x6) -> plus2(x5,x6)
      app(plus(),x6) -> plus1(x6)
      app(s(),x6) -> s1(x6)
      app(times1(x5),x6) -> times2(x5,x6)
      app(times(),x6) -> times1(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)
     Subterm Criterion Processor:
      simple projection:
       pi(times{2,#}) = 0
      problem:
       DPs:
        
       TRS:
        plus2(0(),y) -> y
        plus2(s1(x),y) -> s1(plus2(x,y))
        times2(0(),y) -> 0()
        times2(s1(x),y) -> plus2(times2(x,y),y)
        comp3(f,g,x) -> app(f,app(g,x))
        twice1(f) -> comp2(f,f)
        app(plus1(x5),x6) -> plus2(x5,x6)
        app(plus(),x6) -> plus1(x6)
        app(s(),x6) -> s1(x6)
        app(times1(x5),x6) -> times2(x5,x6)
        app(times(),x6) -> times1(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)
      Qed
     
     DPs:
      plus{2,#}(s1(x),y) -> plus{2,#}(x,y)
     TRS:
      plus2(0(),y) -> y
      plus2(s1(x),y) -> s1(plus2(x,y))
      times2(0(),y) -> 0()
      times2(s1(x),y) -> plus2(times2(x,y),y)
      comp3(f,g,x) -> app(f,app(g,x))
      twice1(f) -> comp2(f,f)
      app(plus1(x5),x6) -> plus2(x5,x6)
      app(plus(),x6) -> plus1(x6)
      app(s(),x6) -> s1(x6)
      app(times1(x5),x6) -> times2(x5,x6)
      app(times(),x6) -> times1(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)
     Subterm Criterion Processor:
      simple projection:
       pi(plus{2,#}) = 0
      problem:
       DPs:
        
       TRS:
        plus2(0(),y) -> y
        plus2(s1(x),y) -> s1(plus2(x,y))
        times2(0(),y) -> 0()
        times2(s1(x),y) -> plus2(times2(x,y),y)
        comp3(f,g,x) -> app(f,app(g,x))
        twice1(f) -> comp2(f,f)
        app(plus1(x5),x6) -> plus2(x5,x6)
        app(plus(),x6) -> plus1(x6)
        app(s(),x6) -> s1(x6)
        app(times1(x5),x6) -> times2(x5,x6)
        app(times(),x6) -> times1(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)
      Qed