YES

Problem:
 app(app(lt(),app(s(),x)),app(s(),y)) -> app(app(lt(),x),y)
 app(app(lt(),0()),app(s(),y)) -> true()
 app(app(lt(),y),0()) -> false()
 app(app(eq(),x),x) -> true()
 app(app(eq(),app(s(),x)),0()) -> false()
 app(app(eq(),0()),app(s(),x)) -> false()
 app(app(member(),w),null()) -> false()
 app(app(member(),w),app(app(app(fork(),x),y),z)) ->
 app(app(app(if(),app(app(lt(),w),y)),app(app(member(),w),x)),app(app
                                                                  (app(if(),app(app(eq(),w),y)),
                                                                   true
                                                                   ()),
                                                                  app(app(member(),w),z)))

Proof:
 DP Processor:
  DPs:
   app#(app(lt(),app(s(),x)),app(s(),y)) -> app#(lt(),x)
   app#(app(lt(),app(s(),x)),app(s(),y)) -> app#(app(lt(),x),y)
   app#(app(member(),w),app(app(app(fork(),x),y),z)) -> app#(app(member(),w),z)
   app#(app(member(),w),app(app(app(fork(),x),y),z)) -> app#(eq(),w)
   app#(app(member(),w),app(app(app(fork(),x),y),z)) -> app#(app(eq(),w),y)
   app#(app(member(),w),app(app(app(fork(),x),y),z)) -> app#(if(),app(app(eq(),w),y))
   app#(app(member(),w),app(app(app(fork(),x),y),z)) -> app#(app(if(),app(app(eq(),w),y)),true())
   app#(app(member(),w),app(app(app(fork(),x),y),z)) ->
   app#(app(app(if(),app(app(eq(),w),y)),true()),app(app(member(),w),z))
   app#(app(member(),w),app(app(app(fork(),x),y),z)) -> app#(app(member(),w),x)
   app#(app(member(),w),app(app(app(fork(),x),y),z)) -> app#(lt(),w)
   app#(app(member(),w),app(app(app(fork(),x),y),z)) -> app#(app(lt(),w),y)
   app#(app(member(),w),app(app(app(fork(),x),y),z)) -> app#(if(),app(app(lt(),w),y))
   app#(app(member(),w),app(app(app(fork(),x),y),z)) ->
   app#(app(if(),app(app(lt(),w),y)),app(app(member(),w),x))
   app#(app(member(),w),app(app(app(fork(),x),y),z)) ->
   app#(app(app(if(),app(app(lt(),w),y)),app(app(member(),w),x)),app(
                                                                    app
                                                                    (
                                                                    app(if(),app(app(eq(),w),y)),
                                                                    true
                                                                    ()),
                                                                    app(app(member(),w),z)))
  TRS:
   app(app(lt(),app(s(),x)),app(s(),y)) -> app(app(lt(),x),y)
   app(app(lt(),0()),app(s(),y)) -> true()
   app(app(lt(),y),0()) -> false()
   app(app(eq(),x),x) -> true()
   app(app(eq(),app(s(),x)),0()) -> false()
   app(app(eq(),0()),app(s(),x)) -> false()
   app(app(member(),w),null()) -> false()
   app(app(member(),w),app(app(app(fork(),x),y),z)) ->
   app(app(app(if(),app(app(lt(),w),y)),app(app(member(),w),x)),app(app
                                                                    (
                                                                    app(if(),app(app(eq(),w),y)),
                                                                    true
                                                                    ()),
                                                                    app(app(member(),w),z)))
  EDG Processor:
   DPs:
    app#(app(lt(),app(s(),x)),app(s(),y)) -> app#(lt(),x)
    app#(app(lt(),app(s(),x)),app(s(),y)) -> app#(app(lt(),x),y)
    app#(app(member(),w),app(app(app(fork(),x),y),z)) -> app#(app(member(),w),z)
    app#(app(member(),w),app(app(app(fork(),x),y),z)) -> app#(eq(),w)
    app#(app(member(),w),app(app(app(fork(),x),y),z)) -> app#(app(eq(),w),y)
    app#(app(member(),w),app(app(app(fork(),x),y),z)) -> app#(if(),app(app(eq(),w),y))
    app#(app(member(),w),app(app(app(fork(),x),y),z)) -> app#(app(if(),app(app(eq(),w),y)),true())
    app#(app(member(),w),app(app(app(fork(),x),y),z)) ->
    app#(app(app(if(),app(app(eq(),w),y)),true()),app(app(member(),w),z))
    app#(app(member(),w),app(app(app(fork(),x),y),z)) -> app#(app(member(),w),x)
    app#(app(member(),w),app(app(app(fork(),x),y),z)) -> app#(lt(),w)
    app#(app(member(),w),app(app(app(fork(),x),y),z)) -> app#(app(lt(),w),y)
    app#(app(member(),w),app(app(app(fork(),x),y),z)) -> app#(if(),app(app(lt(),w),y))
    app#(app(member(),w),app(app(app(fork(),x),y),z)) ->
    app#(app(if(),app(app(lt(),w),y)),app(app(member(),w),x))
    app#(app(member(),w),app(app(app(fork(),x),y),z)) ->
    app#(app(app(if(),app(app(lt(),w),y)),app(app(member(),w),x)),app
                                                                  (app
                                                                   (app(if(),app(app(eq(),w),y)),
                                                                    true
                                                                    ()),
                                                                   app(app(member(),w),z)))
   TRS:
    app(app(lt(),app(s(),x)),app(s(),y)) -> app(app(lt(),x),y)
    app(app(lt(),0()),app(s(),y)) -> true()
    app(app(lt(),y),0()) -> false()
    app(app(eq(),x),x) -> true()
    app(app(eq(),app(s(),x)),0()) -> false()
    app(app(eq(),0()),app(s(),x)) -> false()
    app(app(member(),w),null()) -> false()
    app(app(member(),w),app(app(app(fork(),x),y),z)) ->
    app(app(app(if(),app(app(lt(),w),y)),app(app(member(),w),x)),app(
                                                                    app
                                                                    (
                                                                    app(if(),app(app(eq(),w),y)),
                                                                    true
                                                                    ()),
                                                                    app(app(member(),w),z)))
   graph:
    app#(app(member(),w),app(app(app(fork(),x),y),z)) -> app#(app(member(),w),z) ->
    app#(app(member(),w),app(app(app(fork(),x),y),z)) -> app#(app(member(),w),z)
    app#(app(member(),w),app(app(app(fork(),x),y),z)) -> app#(app(member(),w),z) ->
    app#(app(member(),w),app(app(app(fork(),x),y),z)) -> app#(eq(),w)
    app#(app(member(),w),app(app(app(fork(),x),y),z)) -> app#(app(member(),w),z) ->
    app#(app(member(),w),app(app(app(fork(),x),y),z)) -> app#(app(eq(),w),y)
    app#(app(member(),w),app(app(app(fork(),x),y),z)) -> app#(app(member(),w),z) ->
    app#(app(member(),w),app(app(app(fork(),x),y),z)) -> app#(if(),app(app(eq(),w),y))
    app#(app(member(),w),app(app(app(fork(),x),y),z)) -> app#(app(member(),w),z) ->
    app#(app(member(),w),app(app(app(fork(),x),y),z)) -> app#(app(if(),app(app(eq(),w),y)),true())
    app#(app(member(),w),app(app(app(fork(),x),y),z)) -> app#(app(member(),w),z) ->
    app#(app(member(),w),app(app(app(fork(),x),y),z)) ->
    app#(app(app(if(),app(app(eq(),w),y)),true()),app(app(member(),w),z))
    app#(app(member(),w),app(app(app(fork(),x),y),z)) -> app#(app(member(),w),z) ->
    app#(app(member(),w),app(app(app(fork(),x),y),z)) -> app#(app(member(),w),x)
    app#(app(member(),w),app(app(app(fork(),x),y),z)) -> app#(app(member(),w),z) ->
    app#(app(member(),w),app(app(app(fork(),x),y),z)) -> app#(lt(),w)
    app#(app(member(),w),app(app(app(fork(),x),y),z)) -> app#(app(member(),w),z) ->
    app#(app(member(),w),app(app(app(fork(),x),y),z)) -> app#(app(lt(),w),y)
    app#(app(member(),w),app(app(app(fork(),x),y),z)) -> app#(app(member(),w),z) ->
    app#(app(member(),w),app(app(app(fork(),x),y),z)) -> app#(if(),app(app(lt(),w),y))
    app#(app(member(),w),app(app(app(fork(),x),y),z)) -> app#(app(member(),w),z) ->
    app#(app(member(),w),app(app(app(fork(),x),y),z)) ->
    app#(app(if(),app(app(lt(),w),y)),app(app(member(),w),x))
    app#(app(member(),w),app(app(app(fork(),x),y),z)) -> app#(app(member(),w),z) ->
    app#(app(member(),w),app(app(app(fork(),x),y),z)) ->
    app#(app(app(if(),app(app(lt(),w),y)),app(app(member(),w),x)),app
                                                                  (app
                                                                   (app(if(),app(app(eq(),w),y)),
                                                                    true
                                                                    ()),
                                                                   app(app(member(),w),z)))
    app#(app(member(),w),app(app(app(fork(),x),y),z)) -> app#(app(member(),w),x) ->
    app#(app(member(),w),app(app(app(fork(),x),y),z)) -> app#(app(member(),w),z)
    app#(app(member(),w),app(app(app(fork(),x),y),z)) -> app#(app(member(),w),x) ->
    app#(app(member(),w),app(app(app(fork(),x),y),z)) -> app#(eq(),w)
    app#(app(member(),w),app(app(app(fork(),x),y),z)) -> app#(app(member(),w),x) ->
    app#(app(member(),w),app(app(app(fork(),x),y),z)) -> app#(app(eq(),w),y)
    app#(app(member(),w),app(app(app(fork(),x),y),z)) -> app#(app(member(),w),x) ->
    app#(app(member(),w),app(app(app(fork(),x),y),z)) -> app#(if(),app(app(eq(),w),y))
    app#(app(member(),w),app(app(app(fork(),x),y),z)) -> app#(app(member(),w),x) ->
    app#(app(member(),w),app(app(app(fork(),x),y),z)) -> app#(app(if(),app(app(eq(),w),y)),true())
    app#(app(member(),w),app(app(app(fork(),x),y),z)) -> app#(app(member(),w),x) ->
    app#(app(member(),w),app(app(app(fork(),x),y),z)) ->
    app#(app(app(if(),app(app(eq(),w),y)),true()),app(app(member(),w),z))
    app#(app(member(),w),app(app(app(fork(),x),y),z)) -> app#(app(member(),w),x) ->
    app#(app(member(),w),app(app(app(fork(),x),y),z)) -> app#(app(member(),w),x)
    app#(app(member(),w),app(app(app(fork(),x),y),z)) -> app#(app(member(),w),x) ->
    app#(app(member(),w),app(app(app(fork(),x),y),z)) -> app#(lt(),w)
    app#(app(member(),w),app(app(app(fork(),x),y),z)) -> app#(app(member(),w),x) ->
    app#(app(member(),w),app(app(app(fork(),x),y),z)) -> app#(app(lt(),w),y)
    app#(app(member(),w),app(app(app(fork(),x),y),z)) -> app#(app(member(),w),x) ->
    app#(app(member(),w),app(app(app(fork(),x),y),z)) -> app#(if(),app(app(lt(),w),y))
    app#(app(member(),w),app(app(app(fork(),x),y),z)) -> app#(app(member(),w),x) ->
    app#(app(member(),w),app(app(app(fork(),x),y),z)) ->
    app#(app(if(),app(app(lt(),w),y)),app(app(member(),w),x))
    app#(app(member(),w),app(app(app(fork(),x),y),z)) -> app#(app(member(),w),x) ->
    app#(app(member(),w),app(app(app(fork(),x),y),z)) ->
    app#(app(app(if(),app(app(lt(),w),y)),app(app(member(),w),x)),app
                                                                  (app
                                                                   (app(if(),app(app(eq(),w),y)),
                                                                    true
                                                                    ()),
                                                                   app(app(member(),w),z)))
    app#(app(member(),w),app(app(app(fork(),x),y),z)) -> app#(app(lt(),w),y) ->
    app#(app(lt(),app(s(),x)),app(s(),y)) -> app#(lt(),x)
    app#(app(member(),w),app(app(app(fork(),x),y),z)) -> app#(app(lt(),w),y) ->
    app#(app(lt(),app(s(),x)),app(s(),y)) -> app#(app(lt(),x),y)
    app#(app(lt(),app(s(),x)),app(s(),y)) -> app#(app(lt(),x),y) ->
    app#(app(lt(),app(s(),x)),app(s(),y)) -> app#(lt(),x)
    app#(app(lt(),app(s(),x)),app(s(),y)) -> app#(app(lt(),x),y) ->
    app#(app(lt(),app(s(),x)),app(s(),y)) -> app#(app(lt(),x),y)
   SCC Processor:
    #sccs: 2
    #rules: 3
    #arcs: 28/196
    DPs:
     app#(app(member(),w),app(app(app(fork(),x),y),z)) -> app#(app(member(),w),z)
     app#(app(member(),w),app(app(app(fork(),x),y),z)) -> app#(app(member(),w),x)
    TRS:
     app(app(lt(),app(s(),x)),app(s(),y)) -> app(app(lt(),x),y)
     app(app(lt(),0()),app(s(),y)) -> true()
     app(app(lt(),y),0()) -> false()
     app(app(eq(),x),x) -> true()
     app(app(eq(),app(s(),x)),0()) -> false()
     app(app(eq(),0()),app(s(),x)) -> false()
     app(app(member(),w),null()) -> false()
     app(app(member(),w),app(app(app(fork(),x),y),z)) ->
     app(app(app(if(),app(app(lt(),w),y)),app(app(member(),w),x)),app
                                                                  (app
                                                                   (app(if(),app(app(eq(),w),y)),
                                                                    true
                                                                    ()),
                                                                   app(app(member(),w),z)))
    Subterm Criterion Processor:
     simple projection:
      pi(app#) = 1
     problem:
      DPs:
       
      TRS:
       app(app(lt(),app(s(),x)),app(s(),y)) -> app(app(lt(),x),y)
       app(app(lt(),0()),app(s(),y)) -> true()
       app(app(lt(),y),0()) -> false()
       app(app(eq(),x),x) -> true()
       app(app(eq(),app(s(),x)),0()) -> false()
       app(app(eq(),0()),app(s(),x)) -> false()
       app(app(member(),w),null()) -> false()
       app(app(member(),w),app(app(app(fork(),x),y),z)) ->
       app(app(app(if(),app(app(lt(),w),y)),app(app(member(),w),x)),app
                                                                    (
                                                                    app
                                                                    (
                                                                    app(if(),app(app(eq(),w),y)),
                                                                    true
                                                                    ()),
                                                                    app(app(member(),w),z)))
     Qed
    
    DPs:
     app#(app(lt(),app(s(),x)),app(s(),y)) -> app#(app(lt(),x),y)
    TRS:
     app(app(lt(),app(s(),x)),app(s(),y)) -> app(app(lt(),x),y)
     app(app(lt(),0()),app(s(),y)) -> true()
     app(app(lt(),y),0()) -> false()
     app(app(eq(),x),x) -> true()
     app(app(eq(),app(s(),x)),0()) -> false()
     app(app(eq(),0()),app(s(),x)) -> false()
     app(app(member(),w),null()) -> false()
     app(app(member(),w),app(app(app(fork(),x),y),z)) ->
     app(app(app(if(),app(app(lt(),w),y)),app(app(member(),w),x)),app
                                                                  (app
                                                                   (app(if(),app(app(eq(),w),y)),
                                                                    true
                                                                    ()),
                                                                   app(app(member(),w),z)))
    Subterm Criterion Processor:
     simple projection:
      pi(app#) = 1
     problem:
      DPs:
       
      TRS:
       app(app(lt(),app(s(),x)),app(s(),y)) -> app(app(lt(),x),y)
       app(app(lt(),0()),app(s(),y)) -> true()
       app(app(lt(),y),0()) -> false()
       app(app(eq(),x),x) -> true()
       app(app(eq(),app(s(),x)),0()) -> false()
       app(app(eq(),0()),app(s(),x)) -> false()
       app(app(member(),w),null()) -> false()
       app(app(member(),w),app(app(app(fork(),x),y),z)) ->
       app(app(app(if(),app(app(lt(),w),y)),app(app(member(),w),x)),app
                                                                    (
                                                                    app
                                                                    (
                                                                    app(if(),app(app(eq(),w),y)),
                                                                    true
                                                                    ()),
                                                                    app(app(member(),w),z)))
     Qed