/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(app(consif(),true()),x),ys) -> app(app(cons(),x),ys)
 app(app(app(consif(),false()),x),ys) -> ys
 app(app(filter(),f),nil()) -> nil()
 app(app(filter(),f),app(app(cons(),x),xs)) ->
 app(app(app(consif(),app(f,x)),x),app(app(filter(),f),xs))

Proof:
 Extended Uncurrying Processor:
  application symbol: app
  symbol table:
   nil ==> nil0/0
   filter ==> filter0/0 filter1/1 filter2/2
   false ==> false0/0
   cons ==> cons0/0 cons1/1 cons2/2
   true ==> true0/0
   consif ==> consif0/0 consif1/1 consif2/2 consif3/3
   
  uncurry-rules:
   app(consif2(x4,x5),x6) -> consif3(x4,x5,x6)
   app(consif1(x4),x5) -> consif2(x4,x5)
   app(consif0(),x4) -> consif1(x4)
   app(cons1(x9),x10) -> cons2(x9,x10)
   app(cons0(),x9) -> cons1(x9)
   app(filter1(x13),x14) -> filter2(x13,x14)
   app(filter0(),x13) -> filter1(x13)
  eta-rules:
   
  problem:
   consif3(true0(),x,ys) -> cons2(x,ys)
   consif3(false0(),x,ys) -> ys
   filter2(f,nil0()) -> nil0()
   filter2(f,cons2(x,xs)) -> consif3(app(f,x),x,filter2(f,xs))
   app(consif2(x4,x5),x6) -> consif3(x4,x5,x6)
   app(consif1(x4),x5) -> consif2(x4,x5)
   app(consif0(),x4) -> consif1(x4)
   app(cons1(x9),x10) -> cons2(x9,x10)
   app(cons0(),x9) -> cons1(x9)
   app(filter1(x13),x14) -> filter2(x13,x14)
   app(filter0(),x13) -> filter1(x13)
  DP Processor:
   DPs:
    filter{2,#}(f,cons2(x,xs)) -> filter{2,#}(f,xs)
    filter{2,#}(f,cons2(x,xs)) -> app#(f,x)
    filter{2,#}(f,cons2(x,xs)) -> consif{3,#}(app(f,x),x,filter2(f,xs))
    app#(consif2(x4,x5),x6) -> consif{3,#}(x4,x5,x6)
    app#(filter1(x13),x14) -> filter{2,#}(x13,x14)
   TRS:
    consif3(true0(),x,ys) -> cons2(x,ys)
    consif3(false0(),x,ys) -> ys
    filter2(f,nil0()) -> nil0()
    filter2(f,cons2(x,xs)) -> consif3(app(f,x),x,filter2(f,xs))
    app(consif2(x4,x5),x6) -> consif3(x4,x5,x6)
    app(consif1(x4),x5) -> consif2(x4,x5)
    app(consif0(),x4) -> consif1(x4)
    app(cons1(x9),x10) -> cons2(x9,x10)
    app(cons0(),x9) -> cons1(x9)
    app(filter1(x13),x14) -> filter2(x13,x14)
    app(filter0(),x13) -> filter1(x13)
   TDG Processor:
    DPs:
     filter{2,#}(f,cons2(x,xs)) -> filter{2,#}(f,xs)
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x)
     filter{2,#}(f,cons2(x,xs)) -> consif{3,#}(app(f,x),x,filter2(f,xs))
     app#(consif2(x4,x5),x6) -> consif{3,#}(x4,x5,x6)
     app#(filter1(x13),x14) -> filter{2,#}(x13,x14)
    TRS:
     consif3(true0(),x,ys) -> cons2(x,ys)
     consif3(false0(),x,ys) -> ys
     filter2(f,nil0()) -> nil0()
     filter2(f,cons2(x,xs)) -> consif3(app(f,x),x,filter2(f,xs))
     app(consif2(x4,x5),x6) -> consif3(x4,x5,x6)
     app(consif1(x4),x5) -> consif2(x4,x5)
     app(consif0(),x4) -> consif1(x4)
     app(cons1(x9),x10) -> cons2(x9,x10)
     app(cons0(),x9) -> cons1(x9)
     app(filter1(x13),x14) -> filter2(x13,x14)
     app(filter0(),x13) -> filter1(x13)
    graph:
     app#(filter1(x13),x14) -> filter{2,#}(x13,x14) ->
     filter{2,#}(f,cons2(x,xs)) -> consif{3,#}(app(f,x),x,filter2(f,xs))
     app#(filter1(x13),x14) -> filter{2,#}(x13,x14) ->
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x)
     app#(filter1(x13),x14) -> filter{2,#}(x13,x14) ->
     filter{2,#}(f,cons2(x,xs)) -> filter{2,#}(f,xs)
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(filter1(x13),x14) -> filter{2,#}(x13,x14)
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(consif2(x4,x5),x6) -> consif{3,#}(x4,x5,x6)
     filter{2,#}(f,cons2(x,xs)) -> filter{2,#}(f,xs) ->
     filter{2,#}(f,cons2(x,xs)) -> consif{3,#}(app(f,x),x,filter2(f,xs))
     filter{2,#}(f,cons2(x,xs)) -> filter{2,#}(f,xs) ->
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x)
     filter{2,#}(f,cons2(x,xs)) -> filter{2,#}(f,xs) ->
     filter{2,#}(f,cons2(x,xs)) -> filter{2,#}(f,xs)
    SCC Processor:
     #sccs: 1
     #rules: 3
     #arcs: 8/25
     DPs:
      app#(filter1(x13),x14) -> filter{2,#}(x13,x14)
      filter{2,#}(f,cons2(x,xs)) -> filter{2,#}(f,xs)
      filter{2,#}(f,cons2(x,xs)) -> app#(f,x)
     TRS:
      consif3(true0(),x,ys) -> cons2(x,ys)
      consif3(false0(),x,ys) -> ys
      filter2(f,nil0()) -> nil0()
      filter2(f,cons2(x,xs)) -> consif3(app(f,x),x,filter2(f,xs))
      app(consif2(x4,x5),x6) -> consif3(x4,x5,x6)
      app(consif1(x4),x5) -> consif2(x4,x5)
      app(consif0(),x4) -> consif1(x4)
      app(cons1(x9),x10) -> cons2(x9,x10)
      app(cons0(),x9) -> cons1(x9)
      app(filter1(x13),x14) -> filter2(x13,x14)
      app(filter0(),x13) -> filter1(x13)
     Subterm Criterion Processor:
      simple projection:
       pi(filter{2,#}) = 0
       pi(app#) = 0
      problem:
       DPs:
        filter{2,#}(f,cons2(x,xs)) -> filter{2,#}(f,xs)
        filter{2,#}(f,cons2(x,xs)) -> app#(f,x)
       TRS:
        consif3(true0(),x,ys) -> cons2(x,ys)
        consif3(false0(),x,ys) -> ys
        filter2(f,nil0()) -> nil0()
        filter2(f,cons2(x,xs)) -> consif3(app(f,x),x,filter2(f,xs))
        app(consif2(x4,x5),x6) -> consif3(x4,x5,x6)
        app(consif1(x4),x5) -> consif2(x4,x5)
        app(consif0(),x4) -> consif1(x4)
        app(cons1(x9),x10) -> cons2(x9,x10)
        app(cons0(),x9) -> cons1(x9)
        app(filter1(x13),x14) -> filter2(x13,x14)
        app(filter0(),x13) -> filter1(x13)
      SCC Processor:
       #sccs: 1
       #rules: 1
       #arcs: 5/4
       DPs:
        filter{2,#}(f,cons2(x,xs)) -> filter{2,#}(f,xs)
       TRS:
        consif3(true0(),x,ys) -> cons2(x,ys)
        consif3(false0(),x,ys) -> ys
        filter2(f,nil0()) -> nil0()
        filter2(f,cons2(x,xs)) -> consif3(app(f,x),x,filter2(f,xs))
        app(consif2(x4,x5),x6) -> consif3(x4,x5,x6)
        app(consif1(x4),x5) -> consif2(x4,x5)
        app(consif0(),x4) -> consif1(x4)
        app(cons1(x9),x10) -> cons2(x9,x10)
        app(cons0(),x9) -> cons1(x9)
        app(filter1(x13),x14) -> filter2(x13,x14)
        app(filter0(),x13) -> filter1(x13)
       Subterm Criterion Processor:
        simple projection:
         pi(filter{2,#}) = 1
        problem:
         DPs:
          
         TRS:
          consif3(true0(),x,ys) -> cons2(x,ys)
          consif3(false0(),x,ys) -> ys
          filter2(f,nil0()) -> nil0()
          filter2(f,cons2(x,xs)) -> consif3(app(f,x),x,filter2(f,xs))
          app(consif2(x4,x5),x6) -> consif3(x4,x5,x6)
          app(consif1(x4),x5) -> consif2(x4,x5)
          app(consif0(),x4) -> consif1(x4)
          app(cons1(x9),x10) -> cons2(x9,x10)
          app(cons0(),x9) -> cons1(x9)
          app(filter1(x13),x14) -> filter2(x13,x14)
          app(filter0(),x13) -> filter1(x13)
        Qed