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


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YES

Problem:
 app(app(app(if(),true()),x),y) -> x
 app(app(app(if(),false()),x),y) -> y
 app(app(filter(),f),nil()) -> nil()
 app(app(filter(),f),app(app(cons(),x),xs)) ->
 app(app(app(if(),app(f,x)),app(app(cons(),x),app(app(filter(),f),xs))),app(app(filter(),f),xs))

Proof:
 Extended Uncurrying Processor:
  application symbol: app
  symbol table:
   cons ==> cons0/0 cons1/1 cons2/2
   nil ==> nil0/0
   filter ==> filter0/0 filter1/1 filter2/2
   false ==> false0/0
   true ==> true0/0
   if ==> if0/0 if1/1 if2/2 if3/3
   
  uncurry-rules:
   app(if2(x4,x5),x6) -> if3(x4,x5,x6)
   app(if1(x4),x5) -> if2(x4,x5)
   app(if0(),x4) -> if1(x4)
   app(filter1(x10),x11) -> filter2(x10,x11)
   app(filter0(),x10) -> filter1(x10)
   app(cons1(x14),x15) -> cons2(x14,x15)
   app(cons0(),x14) -> cons1(x14)
  eta-rules:
   
  problem:
   if3(true0(),x,y) -> x
   if3(false0(),x,y) -> y
   filter2(f,nil0()) -> nil0()
   filter2(f,cons2(x,xs)) -> if3(app(f,x),cons2(x,filter2(f,xs)),filter2(f,xs))
   app(if2(x4,x5),x6) -> if3(x4,x5,x6)
   app(if1(x4),x5) -> if2(x4,x5)
   app(if0(),x4) -> if1(x4)
   app(filter1(x10),x11) -> filter2(x10,x11)
   app(filter0(),x10) -> filter1(x10)
   app(cons1(x14),x15) -> cons2(x14,x15)
   app(cons0(),x14) -> cons1(x14)
  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)) -> if{3,#}(app(f,x),cons2(x,filter2(f,xs)),filter2(f,xs))
    app#(if2(x4,x5),x6) -> if{3,#}(x4,x5,x6)
    app#(filter1(x10),x11) -> filter{2,#}(x10,x11)
   TRS:
    if3(true0(),x,y) -> x
    if3(false0(),x,y) -> y
    filter2(f,nil0()) -> nil0()
    filter2(f,cons2(x,xs)) -> if3(app(f,x),cons2(x,filter2(f,xs)),filter2(f,xs))
    app(if2(x4,x5),x6) -> if3(x4,x5,x6)
    app(if1(x4),x5) -> if2(x4,x5)
    app(if0(),x4) -> if1(x4)
    app(filter1(x10),x11) -> filter2(x10,x11)
    app(filter0(),x10) -> filter1(x10)
    app(cons1(x14),x15) -> cons2(x14,x15)
    app(cons0(),x14) -> cons1(x14)
   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)) -> if{3,#}(app(f,x),cons2(x,filter2(f,xs)),filter2(f,xs))
     app#(if2(x4,x5),x6) -> if{3,#}(x4,x5,x6)
     app#(filter1(x10),x11) -> filter{2,#}(x10,x11)
    TRS:
     if3(true0(),x,y) -> x
     if3(false0(),x,y) -> y
     filter2(f,nil0()) -> nil0()
     filter2(f,cons2(x,xs)) -> if3(app(f,x),cons2(x,filter2(f,xs)),filter2(f,xs))
     app(if2(x4,x5),x6) -> if3(x4,x5,x6)
     app(if1(x4),x5) -> if2(x4,x5)
     app(if0(),x4) -> if1(x4)
     app(filter1(x10),x11) -> filter2(x10,x11)
     app(filter0(),x10) -> filter1(x10)
     app(cons1(x14),x15) -> cons2(x14,x15)
     app(cons0(),x14) -> cons1(x14)
    graph:
     app#(filter1(x10),x11) -> filter{2,#}(x10,x11) ->
     filter{2,#}(f,cons2(x,xs)) -> if{3,#}(app(f,x),cons2(x,filter2(f,xs)),filter2(f,xs))
     app#(filter1(x10),x11) -> filter{2,#}(x10,x11) ->
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x)
     app#(filter1(x10),x11) -> filter{2,#}(x10,x11) ->
     filter{2,#}(f,cons2(x,xs)) -> filter{2,#}(f,xs)
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(filter1(x10),x11) -> filter{2,#}(x10,x11)
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(if2(x4,x5),x6) -> if{3,#}(x4,x5,x6)
     filter{2,#}(f,cons2(x,xs)) -> filter{2,#}(f,xs) ->
     filter{2,#}(f,cons2(x,xs)) -> if{3,#}(app(f,x),cons2(x,filter2(f,xs)),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(x10),x11) -> filter{2,#}(x10,x11)
      filter{2,#}(f,cons2(x,xs)) -> filter{2,#}(f,xs)
      filter{2,#}(f,cons2(x,xs)) -> app#(f,x)
     TRS:
      if3(true0(),x,y) -> x
      if3(false0(),x,y) -> y
      filter2(f,nil0()) -> nil0()
      filter2(f,cons2(x,xs)) -> if3(app(f,x),cons2(x,filter2(f,xs)),filter2(f,xs))
      app(if2(x4,x5),x6) -> if3(x4,x5,x6)
      app(if1(x4),x5) -> if2(x4,x5)
      app(if0(),x4) -> if1(x4)
      app(filter1(x10),x11) -> filter2(x10,x11)
      app(filter0(),x10) -> filter1(x10)
      app(cons1(x14),x15) -> cons2(x14,x15)
      app(cons0(),x14) -> cons1(x14)
     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:
        if3(true0(),x,y) -> x
        if3(false0(),x,y) -> y
        filter2(f,nil0()) -> nil0()
        filter2(f,cons2(x,xs)) -> if3(app(f,x),cons2(x,filter2(f,xs)),filter2(f,xs))
        app(if2(x4,x5),x6) -> if3(x4,x5,x6)
        app(if1(x4),x5) -> if2(x4,x5)
        app(if0(),x4) -> if1(x4)
        app(filter1(x10),x11) -> filter2(x10,x11)
        app(filter0(),x10) -> filter1(x10)
        app(cons1(x14),x15) -> cons2(x14,x15)
        app(cons0(),x14) -> cons1(x14)
      SCC Processor:
       #sccs: 1
       #rules: 1
       #arcs: 5/4
       DPs:
        filter{2,#}(f,cons2(x,xs)) -> filter{2,#}(f,xs)
       TRS:
        if3(true0(),x,y) -> x
        if3(false0(),x,y) -> y
        filter2(f,nil0()) -> nil0()
        filter2(f,cons2(x,xs)) -> if3(app(f,x),cons2(x,filter2(f,xs)),filter2(f,xs))
        app(if2(x4,x5),x6) -> if3(x4,x5,x6)
        app(if1(x4),x5) -> if2(x4,x5)
        app(if0(),x4) -> if1(x4)
        app(filter1(x10),x11) -> filter2(x10,x11)
        app(filter0(),x10) -> filter1(x10)
        app(cons1(x14),x15) -> cons2(x14,x15)
        app(cons0(),x14) -> cons1(x14)
       Subterm Criterion Processor:
        simple projection:
         pi(filter{2,#}) = 1
        problem:
         DPs:
          
         TRS:
          if3(true0(),x,y) -> x
          if3(false0(),x,y) -> y
          filter2(f,nil0()) -> nil0()
          filter2(f,cons2(x,xs)) -> if3(app(f,x),cons2(x,filter2(f,xs)),filter2(f,xs))
          app(if2(x4,x5),x6) -> if3(x4,x5,x6)
          app(if1(x4),x5) -> if2(x4,x5)
          app(if0(),x4) -> if1(x4)
          app(filter1(x10),x11) -> filter2(x10,x11)
          app(filter0(),x10) -> filter1(x10)
          app(cons1(x14),x15) -> cons2(x14,x15)
          app(cons0(),x14) -> cons1(x14)
        Qed