/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(filter(),f),nil()) -> nil()
 app(app(filter(),f),app(app(cons(),y),ys)) ->
 app(app(app(filtersub(),app(f,y)),f),app(app(cons(),y),ys))
 app(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) ->
 app(app(cons(),y),app(app(filter(),f),ys))
 app(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app(app(filter(),f),ys)

Proof:
 Extended Uncurrying Processor:
  application symbol: app
  symbol table:
   false ==> false0/0
   true ==> true0/0
   filtersub ==> filtersub0/0 filtersub1/1 filtersub2/2 filtersub3/3
   cons ==> cons0/0 cons1/1 cons2/2
   nil ==> nil0/0
   filter ==> filter0/0 filter1/1 filter2/2
   
  uncurry-rules:
   app(filter1(x3),x4) -> filter2(x3,x4)
   app(filter0(),x3) -> filter1(x3)
   app(cons1(x7),x8) -> cons2(x7,x8)
   app(cons0(),x7) -> cons1(x7)
   app(filtersub2(x10,x11),x12) -> filtersub3(x10,x11,x12)
   app(filtersub1(x10),x11) -> filtersub2(x10,x11)
   app(filtersub0(),x10) -> filtersub1(x10)
  eta-rules:
   
  problem:
   filter2(f,nil0()) -> nil0()
   filter2(f,cons2(y,ys)) -> filtersub3(app(f,y),f,cons2(y,ys))
   filtersub3(true0(),f,cons2(y,ys)) -> cons2(y,filter2(f,ys))
   filtersub3(false0(),f,cons2(y,ys)) -> filter2(f,ys)
   app(filter1(x3),x4) -> filter2(x3,x4)
   app(filter0(),x3) -> filter1(x3)
   app(cons1(x7),x8) -> cons2(x7,x8)
   app(cons0(),x7) -> cons1(x7)
   app(filtersub2(x10,x11),x12) -> filtersub3(x10,x11,x12)
   app(filtersub1(x10),x11) -> filtersub2(x10,x11)
   app(filtersub0(),x10) -> filtersub1(x10)
  DP Processor:
   DPs:
    filter{2,#}(f,cons2(y,ys)) -> app#(f,y)
    filter{2,#}(f,cons2(y,ys)) -> filtersub{3,#}(app(f,y),f,cons2(y,ys))
    filtersub{3,#}(true0(),f,cons2(y,ys)) -> filter{2,#}(f,ys)
    filtersub{3,#}(false0(),f,cons2(y,ys)) -> filter{2,#}(f,ys)
    app#(filter1(x3),x4) -> filter{2,#}(x3,x4)
    app#(filtersub2(x10,x11),x12) -> filtersub{3,#}(x10,x11,x12)
   TRS:
    filter2(f,nil0()) -> nil0()
    filter2(f,cons2(y,ys)) -> filtersub3(app(f,y),f,cons2(y,ys))
    filtersub3(true0(),f,cons2(y,ys)) -> cons2(y,filter2(f,ys))
    filtersub3(false0(),f,cons2(y,ys)) -> filter2(f,ys)
    app(filter1(x3),x4) -> filter2(x3,x4)
    app(filter0(),x3) -> filter1(x3)
    app(cons1(x7),x8) -> cons2(x7,x8)
    app(cons0(),x7) -> cons1(x7)
    app(filtersub2(x10,x11),x12) -> filtersub3(x10,x11,x12)
    app(filtersub1(x10),x11) -> filtersub2(x10,x11)
    app(filtersub0(),x10) -> filtersub1(x10)
   TDG Processor:
    DPs:
     filter{2,#}(f,cons2(y,ys)) -> app#(f,y)
     filter{2,#}(f,cons2(y,ys)) -> filtersub{3,#}(app(f,y),f,cons2(y,ys))
     filtersub{3,#}(true0(),f,cons2(y,ys)) -> filter{2,#}(f,ys)
     filtersub{3,#}(false0(),f,cons2(y,ys)) -> filter{2,#}(f,ys)
     app#(filter1(x3),x4) -> filter{2,#}(x3,x4)
     app#(filtersub2(x10,x11),x12) -> filtersub{3,#}(x10,x11,x12)
    TRS:
     filter2(f,nil0()) -> nil0()
     filter2(f,cons2(y,ys)) -> filtersub3(app(f,y),f,cons2(y,ys))
     filtersub3(true0(),f,cons2(y,ys)) -> cons2(y,filter2(f,ys))
     filtersub3(false0(),f,cons2(y,ys)) -> filter2(f,ys)
     app(filter1(x3),x4) -> filter2(x3,x4)
     app(filter0(),x3) -> filter1(x3)
     app(cons1(x7),x8) -> cons2(x7,x8)
     app(cons0(),x7) -> cons1(x7)
     app(filtersub2(x10,x11),x12) -> filtersub3(x10,x11,x12)
     app(filtersub1(x10),x11) -> filtersub2(x10,x11)
     app(filtersub0(),x10) -> filtersub1(x10)
    graph:
     filtersub{3,#}(false0(),f,cons2(y,ys)) -> filter{2,#}(f,ys) ->
     filter{2,#}(f,cons2(y,ys)) -> filtersub{3,#}(app(f,y),f,cons2(y,ys))
     filtersub{3,#}(false0(),f,cons2(y,ys)) -> filter{2,#}(f,ys) ->
     filter{2,#}(f,cons2(y,ys)) -> app#(f,y)
     filtersub{3,#}(true0(),f,cons2(y,ys)) -> filter{2,#}(f,ys) ->
     filter{2,#}(f,cons2(y,ys)) -> filtersub{3,#}(app(f,y),f,cons2(y,ys))
     filtersub{3,#}(true0(),f,cons2(y,ys)) -> filter{2,#}(f,ys) ->
     filter{2,#}(f,cons2(y,ys)) -> app#(f,y)
     app#(filtersub2(x10,x11),x12) -> filtersub{3,#}(x10,x11,x12) ->
     filtersub{3,#}(false0(),f,cons2(y,ys)) -> filter{2,#}(f,ys)
     app#(filtersub2(x10,x11),x12) -> filtersub{3,#}(x10,x11,x12) ->
     filtersub{3,#}(true0(),f,cons2(y,ys)) -> filter{2,#}(f,ys)
     app#(filter1(x3),x4) -> filter{2,#}(x3,x4) ->
     filter{2,#}(f,cons2(y,ys)) -> filtersub{3,#}(app(f,y),f,cons2(y,ys))
     app#(filter1(x3),x4) -> filter{2,#}(x3,x4) ->
     filter{2,#}(f,cons2(y,ys)) -> app#(f,y)
     filter{2,#}(f,cons2(y,ys)) -> filtersub{3,#}(app(f,y),f,cons2(y,ys)) ->
     filtersub{3,#}(false0(),f,cons2(y,ys)) -> filter{2,#}(f,ys)
     filter{2,#}(f,cons2(y,ys)) -> filtersub{3,#}(app(f,y),f,cons2(y,ys)) ->
     filtersub{3,#}(true0(),f,cons2(y,ys)) -> filter{2,#}(f,ys)
     filter{2,#}(f,cons2(y,ys)) -> app#(f,y) ->
     app#(filtersub2(x10,x11),x12) -> filtersub{3,#}(x10,x11,x12)
     filter{2,#}(f,cons2(y,ys)) -> app#(f,y) -> app#(filter1(x3),x4) -> filter{2,#}(x3,x4)
    Subterm Criterion Processor:
     simple projection:
      pi(filter{2,#}) = 0
      pi(app#) = 0
      pi(filtersub{3,#}) = 1
     problem:
      DPs:
       filter{2,#}(f,cons2(y,ys)) -> app#(f,y)
       filter{2,#}(f,cons2(y,ys)) -> filtersub{3,#}(app(f,y),f,cons2(y,ys))
       filtersub{3,#}(true0(),f,cons2(y,ys)) -> filter{2,#}(f,ys)
       filtersub{3,#}(false0(),f,cons2(y,ys)) -> filter{2,#}(f,ys)
      TRS:
       filter2(f,nil0()) -> nil0()
       filter2(f,cons2(y,ys)) -> filtersub3(app(f,y),f,cons2(y,ys))
       filtersub3(true0(),f,cons2(y,ys)) -> cons2(y,filter2(f,ys))
       filtersub3(false0(),f,cons2(y,ys)) -> filter2(f,ys)
       app(filter1(x3),x4) -> filter2(x3,x4)
       app(filter0(),x3) -> filter1(x3)
       app(cons1(x7),x8) -> cons2(x7,x8)
       app(cons0(),x7) -> cons1(x7)
       app(filtersub2(x10,x11),x12) -> filtersub3(x10,x11,x12)
       app(filtersub1(x10),x11) -> filtersub2(x10,x11)
       app(filtersub0(),x10) -> filtersub1(x10)
     SCC Processor:
      #sccs: 1
      #rules: 3
      #arcs: 12/16
      DPs:
       filtersub{3,#}(false0(),f,cons2(y,ys)) -> filter{2,#}(f,ys)
       filter{2,#}(f,cons2(y,ys)) -> filtersub{3,#}(app(f,y),f,cons2(y,ys))
       filtersub{3,#}(true0(),f,cons2(y,ys)) -> filter{2,#}(f,ys)
      TRS:
       filter2(f,nil0()) -> nil0()
       filter2(f,cons2(y,ys)) -> filtersub3(app(f,y),f,cons2(y,ys))
       filtersub3(true0(),f,cons2(y,ys)) -> cons2(y,filter2(f,ys))
       filtersub3(false0(),f,cons2(y,ys)) -> filter2(f,ys)
       app(filter1(x3),x4) -> filter2(x3,x4)
       app(filter0(),x3) -> filter1(x3)
       app(cons1(x7),x8) -> cons2(x7,x8)
       app(cons0(),x7) -> cons1(x7)
       app(filtersub2(x10,x11),x12) -> filtersub3(x10,x11,x12)
       app(filtersub1(x10),x11) -> filtersub2(x10,x11)
       app(filtersub0(),x10) -> filtersub1(x10)
      Subterm Criterion Processor:
       simple projection:
        pi(filter{2,#}) = 1
        pi(filtersub{3,#}) = 2
       problem:
        DPs:
         filter{2,#}(f,cons2(y,ys)) -> filtersub{3,#}(app(f,y),f,cons2(y,ys))
        TRS:
         filter2(f,nil0()) -> nil0()
         filter2(f,cons2(y,ys)) -> filtersub3(app(f,y),f,cons2(y,ys))
         filtersub3(true0(),f,cons2(y,ys)) -> cons2(y,filter2(f,ys))
         filtersub3(false0(),f,cons2(y,ys)) -> filter2(f,ys)
         app(filter1(x3),x4) -> filter2(x3,x4)
         app(filter0(),x3) -> filter1(x3)
         app(cons1(x7),x8) -> cons2(x7,x8)
         app(cons0(),x7) -> cons1(x7)
         app(filtersub2(x10,x11),x12) -> filtersub3(x10,x11,x12)
         app(filtersub1(x10),x11) -> filtersub2(x10,x11)
         app(filtersub0(),x10) -> filtersub1(x10)
       SCC Processor:
        #sccs: 0
        #rules: 0
        #arcs: 4/1