/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

Problem:
 app(app(twice(),f),x) -> app(f,app(f,x))
 app(app(map(),f),nil()) -> nil()
 app(app(map(),f),app(app(cons(),h),t)) -> app(app(cons(),app(f,h)),app(app(map(),f),t))
 app(app(fmap(),nil()),x) -> nil()
 app(app(fmap(),app(app(cons(),f),t_f())),x) -> app(app(cons(),app(f,x)),app(app(fmap(),t_f()),x))

Proof:
 Extended Uncurrying Processor:
  application symbol: app
  symbol table:
   t_f ==> t_f0/0
   fmap ==> fmap0/0 fmap1/1 fmap2/2
   cons ==> cons0/0 cons1/1 cons2/2
   nil ==> nil0/0
   map ==> map0/0 map1/1 map2/2
   twice ==> twice0/0 twice1/1 twice2/2
   
  uncurry-rules:
   app(twice1(x4),x5) -> twice2(x4,x5)
   app(twice0(),x4) -> twice1(x4)
   app(map1(x7),x8) -> map2(x7,x8)
   app(map0(),x7) -> map1(x7)
   app(cons1(x11),x12) -> cons2(x11,x12)
   app(cons0(),x11) -> cons1(x11)
   app(fmap1(x14),x15) -> fmap2(x14,x15)
   app(fmap0(),x14) -> fmap1(x14)
  eta-rules:
   
  problem:
   twice2(f,x) -> app(f,app(f,x))
   map2(f,nil0()) -> nil0()
   map2(f,cons2(h,t)) -> cons2(app(f,h),map2(f,t))
   fmap2(nil0(),x) -> nil0()
   fmap2(cons2(f,t_f0()),x) -> cons2(app(f,x),fmap2(t_f0(),x))
   app(twice1(x4),x5) -> twice2(x4,x5)
   app(twice0(),x4) -> twice1(x4)
   app(map1(x7),x8) -> map2(x7,x8)
   app(map0(),x7) -> map1(x7)
   app(cons1(x11),x12) -> cons2(x11,x12)
   app(cons0(),x11) -> cons1(x11)
   app(fmap1(x14),x15) -> fmap2(x14,x15)
   app(fmap0(),x14) -> fmap1(x14)
  DP Processor:
   DPs:
    twice{2,#}(f,x) -> app#(f,x)
    twice{2,#}(f,x) -> app#(f,app(f,x))
    map{2,#}(f,cons2(h,t)) -> map{2,#}(f,t)
    map{2,#}(f,cons2(h,t)) -> app#(f,h)
    fmap{2,#}(cons2(f,t_f0()),x) -> fmap{2,#}(t_f0(),x)
    fmap{2,#}(cons2(f,t_f0()),x) -> app#(f,x)
    app#(twice1(x4),x5) -> twice{2,#}(x4,x5)
    app#(map1(x7),x8) -> map{2,#}(x7,x8)
    app#(fmap1(x14),x15) -> fmap{2,#}(x14,x15)
   TRS:
    twice2(f,x) -> app(f,app(f,x))
    map2(f,nil0()) -> nil0()
    map2(f,cons2(h,t)) -> cons2(app(f,h),map2(f,t))
    fmap2(nil0(),x) -> nil0()
    fmap2(cons2(f,t_f0()),x) -> cons2(app(f,x),fmap2(t_f0(),x))
    app(twice1(x4),x5) -> twice2(x4,x5)
    app(twice0(),x4) -> twice1(x4)
    app(map1(x7),x8) -> map2(x7,x8)
    app(map0(),x7) -> map1(x7)
    app(cons1(x11),x12) -> cons2(x11,x12)
    app(cons0(),x11) -> cons1(x11)
    app(fmap1(x14),x15) -> fmap2(x14,x15)
    app(fmap0(),x14) -> fmap1(x14)
   TDG Processor:
    DPs:
     twice{2,#}(f,x) -> app#(f,x)
     twice{2,#}(f,x) -> app#(f,app(f,x))
     map{2,#}(f,cons2(h,t)) -> map{2,#}(f,t)
     map{2,#}(f,cons2(h,t)) -> app#(f,h)
     fmap{2,#}(cons2(f,t_f0()),x) -> fmap{2,#}(t_f0(),x)
     fmap{2,#}(cons2(f,t_f0()),x) -> app#(f,x)
     app#(twice1(x4),x5) -> twice{2,#}(x4,x5)
     app#(map1(x7),x8) -> map{2,#}(x7,x8)
     app#(fmap1(x14),x15) -> fmap{2,#}(x14,x15)
    TRS:
     twice2(f,x) -> app(f,app(f,x))
     map2(f,nil0()) -> nil0()
     map2(f,cons2(h,t)) -> cons2(app(f,h),map2(f,t))
     fmap2(nil0(),x) -> nil0()
     fmap2(cons2(f,t_f0()),x) -> cons2(app(f,x),fmap2(t_f0(),x))
     app(twice1(x4),x5) -> twice2(x4,x5)
     app(twice0(),x4) -> twice1(x4)
     app(map1(x7),x8) -> map2(x7,x8)
     app(map0(),x7) -> map1(x7)
     app(cons1(x11),x12) -> cons2(x11,x12)
     app(cons0(),x11) -> cons1(x11)
     app(fmap1(x14),x15) -> fmap2(x14,x15)
     app(fmap0(),x14) -> fmap1(x14)
    graph:
     fmap{2,#}(cons2(f,t_f0()),x) -> fmap{2,#}(t_f0(),x) ->
     fmap{2,#}(cons2(f,t_f0()),x) -> app#(f,x)
     fmap{2,#}(cons2(f,t_f0()),x) -> fmap{2,#}(t_f0(),x) ->
     fmap{2,#}(cons2(f,t_f0()),x) -> fmap{2,#}(t_f0(),x)
     fmap{2,#}(cons2(f,t_f0()),x) -> app#(f,x) ->
     app#(fmap1(x14),x15) -> fmap{2,#}(x14,x15)
     fmap{2,#}(cons2(f,t_f0()),x) -> app#(f,x) ->
     app#(map1(x7),x8) -> map{2,#}(x7,x8)
     fmap{2,#}(cons2(f,t_f0()),x) -> app#(f,x) ->
     app#(twice1(x4),x5) -> twice{2,#}(x4,x5)
     map{2,#}(f,cons2(h,t)) -> map{2,#}(f,t) ->
     map{2,#}(f,cons2(h,t)) -> app#(f,h)
     map{2,#}(f,cons2(h,t)) -> map{2,#}(f,t) ->
     map{2,#}(f,cons2(h,t)) -> map{2,#}(f,t)
     map{2,#}(f,cons2(h,t)) -> app#(f,h) ->
     app#(fmap1(x14),x15) -> fmap{2,#}(x14,x15)
     map{2,#}(f,cons2(h,t)) -> app#(f,h) ->
     app#(map1(x7),x8) -> map{2,#}(x7,x8)
     map{2,#}(f,cons2(h,t)) -> app#(f,h) ->
     app#(twice1(x4),x5) -> twice{2,#}(x4,x5)
     app#(fmap1(x14),x15) -> fmap{2,#}(x14,x15) ->
     fmap{2,#}(cons2(f,t_f0()),x) -> app#(f,x)
     app#(fmap1(x14),x15) -> fmap{2,#}(x14,x15) ->
     fmap{2,#}(cons2(f,t_f0()),x) -> fmap{2,#}(t_f0(),x)
     app#(map1(x7),x8) -> map{2,#}(x7,x8) ->
     map{2,#}(f,cons2(h,t)) -> app#(f,h)
     app#(map1(x7),x8) -> map{2,#}(x7,x8) ->
     map{2,#}(f,cons2(h,t)) -> map{2,#}(f,t)
     app#(twice1(x4),x5) -> twice{2,#}(x4,x5) ->
     twice{2,#}(f,x) -> app#(f,app(f,x))
     app#(twice1(x4),x5) -> twice{2,#}(x4,x5) ->
     twice{2,#}(f,x) -> app#(f,x)
     twice{2,#}(f,x) -> app#(f,app(f,x)) ->
     app#(fmap1(x14),x15) -> fmap{2,#}(x14,x15)
     twice{2,#}(f,x) -> app#(f,app(f,x)) ->
     app#(map1(x7),x8) -> map{2,#}(x7,x8)
     twice{2,#}(f,x) -> app#(f,app(f,x)) ->
     app#(twice1(x4),x5) -> twice{2,#}(x4,x5)
     twice{2,#}(f,x) -> app#(f,x) ->
     app#(fmap1(x14),x15) -> fmap{2,#}(x14,x15)
     twice{2,#}(f,x) -> app#(f,x) ->
     app#(map1(x7),x8) -> map{2,#}(x7,x8)
     twice{2,#}(f,x) -> app#(f,x) -> app#(twice1(x4),x5) -> twice{2,#}(x4,x5)
    Subterm Criterion Processor:
     simple projection:
      pi(twice{2,#}) = 0
      pi(app#) = 0
      pi(map{2,#}) = 0
      pi(fmap{2,#}) = 0
     problem:
      DPs:
       twice{2,#}(f,x) -> app#(f,x)
       twice{2,#}(f,x) -> app#(f,app(f,x))
       map{2,#}(f,cons2(h,t)) -> map{2,#}(f,t)
       map{2,#}(f,cons2(h,t)) -> app#(f,h)
      TRS:
       twice2(f,x) -> app(f,app(f,x))
       map2(f,nil0()) -> nil0()
       map2(f,cons2(h,t)) -> cons2(app(f,h),map2(f,t))
       fmap2(nil0(),x) -> nil0()
       fmap2(cons2(f,t_f0()),x) -> cons2(app(f,x),fmap2(t_f0(),x))
       app(twice1(x4),x5) -> twice2(x4,x5)
       app(twice0(),x4) -> twice1(x4)
       app(map1(x7),x8) -> map2(x7,x8)
       app(map0(),x7) -> map1(x7)
       app(cons1(x11),x12) -> cons2(x11,x12)
       app(cons0(),x11) -> cons1(x11)
       app(fmap1(x14),x15) -> fmap2(x14,x15)
       app(fmap0(),x14) -> fmap1(x14)
     SCC Processor:
      #sccs: 1
      #rules: 1
      #arcs: 22/16
      DPs:
       map{2,#}(f,cons2(h,t)) -> map{2,#}(f,t)
      TRS:
       twice2(f,x) -> app(f,app(f,x))
       map2(f,nil0()) -> nil0()
       map2(f,cons2(h,t)) -> cons2(app(f,h),map2(f,t))
       fmap2(nil0(),x) -> nil0()
       fmap2(cons2(f,t_f0()),x) -> cons2(app(f,x),fmap2(t_f0(),x))
       app(twice1(x4),x5) -> twice2(x4,x5)
       app(twice0(),x4) -> twice1(x4)
       app(map1(x7),x8) -> map2(x7,x8)
       app(map0(),x7) -> map1(x7)
       app(cons1(x11),x12) -> cons2(x11,x12)
       app(cons0(),x11) -> cons1(x11)
       app(fmap1(x14),x15) -> fmap2(x14,x15)
       app(fmap0(),x14) -> fmap1(x14)
      Subterm Criterion Processor:
       simple projection:
        pi(map{2,#}) = 1
       problem:
        DPs:
         
        TRS:
         twice2(f,x) -> app(f,app(f,x))
         map2(f,nil0()) -> nil0()
         map2(f,cons2(h,t)) -> cons2(app(f,h),map2(f,t))
         fmap2(nil0(),x) -> nil0()
         fmap2(cons2(f,t_f0()),x) -> cons2(app(f,x),fmap2(t_f0(),x))
         app(twice1(x4),x5) -> twice2(x4,x5)
         app(twice0(),x4) -> twice1(x4)
         app(map1(x7),x8) -> map2(x7,x8)
         app(map0(),x7) -> map1(x7)
         app(cons1(x11),x12) -> cons2(x11,x12)
         app(cons0(),x11) -> cons1(x11)
         app(fmap1(x14),x15) -> fmap2(x14,x15)
         app(fmap0(),x14) -> fmap1(x14)
       Qed