/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(neq(),0()),0()) -> false()
 app(app(neq(),0()),app(s(),y)) -> true()
 app(app(neq(),app(s(),x)),0()) -> true()
 app(app(neq(),app(s(),x)),app(s(),y)) -> app(app(neq(),x),y)
 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)
 nonzero() -> app(filter(),app(neq(),0()))

Proof:
 Extended Uncurrying Processor:
  application symbol: app
  symbol table:
   nonzero ==> nonzero0/0
   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
   true ==> true0/0
   s ==> s0/0 s1/1
   false ==> false0/0
   0 ==> 00/0
   neq ==> neq0/0 neq1/1 neq2/2
   
  uncurry-rules:
   app(neq1(x4),x5) -> neq2(x4,x5)
   app(neq0(),x4) -> neq1(x4)
   app(s0(),x9) -> s1(x9)
   app(filter1(x12),x13) -> filter2(x12,x13)
   app(filter0(),x12) -> filter1(x12)
   app(cons1(x16),x17) -> cons2(x16,x17)
   app(cons0(),x16) -> cons1(x16)
   app(filtersub2(x19,x20),x21) -> filtersub3(x19,x20,x21)
   app(filtersub1(x19),x20) -> filtersub2(x19,x20)
   app(filtersub0(),x19) -> filtersub1(x19)
  eta-rules:
   
  problem:
   neq2(00(),00()) -> false0()
   neq2(00(),s1(y)) -> true0()
   neq2(s1(x),00()) -> true0()
   neq2(s1(x),s1(y)) -> neq2(x,y)
   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)
   nonzero0() -> filter1(neq1(00()))
   app(neq1(x4),x5) -> neq2(x4,x5)
   app(neq0(),x4) -> neq1(x4)
   app(s0(),x9) -> s1(x9)
   app(filter1(x12),x13) -> filter2(x12,x13)
   app(filter0(),x12) -> filter1(x12)
   app(cons1(x16),x17) -> cons2(x16,x17)
   app(cons0(),x16) -> cons1(x16)
   app(filtersub2(x19,x20),x21) -> filtersub3(x19,x20,x21)
   app(filtersub1(x19),x20) -> filtersub2(x19,x20)
   app(filtersub0(),x19) -> filtersub1(x19)
  DP Processor:
   DPs:
    neq{2,#}(s1(x),s1(y)) -> neq{2,#}(x,y)
    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#(neq1(x4),x5) -> neq{2,#}(x4,x5)
    app#(filter1(x12),x13) -> filter{2,#}(x12,x13)
    app#(filtersub2(x19,x20),x21) -> filtersub{3,#}(x19,x20,x21)
   TRS:
    neq2(00(),00()) -> false0()
    neq2(00(),s1(y)) -> true0()
    neq2(s1(x),00()) -> true0()
    neq2(s1(x),s1(y)) -> neq2(x,y)
    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)
    nonzero0() -> filter1(neq1(00()))
    app(neq1(x4),x5) -> neq2(x4,x5)
    app(neq0(),x4) -> neq1(x4)
    app(s0(),x9) -> s1(x9)
    app(filter1(x12),x13) -> filter2(x12,x13)
    app(filter0(),x12) -> filter1(x12)
    app(cons1(x16),x17) -> cons2(x16,x17)
    app(cons0(),x16) -> cons1(x16)
    app(filtersub2(x19,x20),x21) -> filtersub3(x19,x20,x21)
    app(filtersub1(x19),x20) -> filtersub2(x19,x20)
    app(filtersub0(),x19) -> filtersub1(x19)
   TDG Processor:
    DPs:
     neq{2,#}(s1(x),s1(y)) -> neq{2,#}(x,y)
     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#(neq1(x4),x5) -> neq{2,#}(x4,x5)
     app#(filter1(x12),x13) -> filter{2,#}(x12,x13)
     app#(filtersub2(x19,x20),x21) -> filtersub{3,#}(x19,x20,x21)
    TRS:
     neq2(00(),00()) -> false0()
     neq2(00(),s1(y)) -> true0()
     neq2(s1(x),00()) -> true0()
     neq2(s1(x),s1(y)) -> neq2(x,y)
     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)
     nonzero0() -> filter1(neq1(00()))
     app(neq1(x4),x5) -> neq2(x4,x5)
     app(neq0(),x4) -> neq1(x4)
     app(s0(),x9) -> s1(x9)
     app(filter1(x12),x13) -> filter2(x12,x13)
     app(filter0(),x12) -> filter1(x12)
     app(cons1(x16),x17) -> cons2(x16,x17)
     app(cons0(),x16) -> cons1(x16)
     app(filtersub2(x19,x20),x21) -> filtersub3(x19,x20,x21)
     app(filtersub1(x19),x20) -> filtersub2(x19,x20)
     app(filtersub0(),x19) -> filtersub1(x19)
    graph:
     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)
     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)
     app#(filtersub2(x19,x20),x21) -> filtersub{3,#}(x19,x20,x21) ->
     filtersub{3,#}(false0(),f,cons2(y,ys)) -> filter{2,#}(f,ys)
     app#(filtersub2(x19,x20),x21) -> filtersub{3,#}(x19,x20,x21) ->
     filtersub{3,#}(true0(),f,cons2(y,ys)) -> filter{2,#}(f,ys)
     app#(filter1(x12),x13) -> filter{2,#}(x12,x13) ->
     filter{2,#}(f,cons2(y,ys)) -> filtersub{3,#}(app(f,y),f,cons2(y,ys))
     app#(filter1(x12),x13) -> filter{2,#}(x12,x13) ->
     filter{2,#}(f,cons2(y,ys)) -> app#(f,y)
     app#(neq1(x4),x5) -> neq{2,#}(x4,x5) ->
     neq{2,#}(s1(x),s1(y)) -> neq{2,#}(x,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(x19,x20),x21) -> filtersub{3,#}(x19,x20,x21)
     filter{2,#}(f,cons2(y,ys)) -> app#(f,y) ->
     app#(filter1(x12),x13) -> filter{2,#}(x12,x13)
     filter{2,#}(f,cons2(y,ys)) -> app#(f,y) ->
     app#(neq1(x4),x5) -> neq{2,#}(x4,x5)
     neq{2,#}(s1(x),s1(y)) -> neq{2,#}(x,y) -> neq{2,#}(s1(x),s1(y)) -> neq{2,#}(x,y)
    SCC Processor:
     #sccs: 2
     #rules: 7
     #arcs: 15/64
     DPs:
      filtersub{3,#}(true0(),f,cons2(y,ys)) -> filter{2,#}(f,ys)
      filter{2,#}(f,cons2(y,ys)) -> app#(f,y)
      app#(filter1(x12),x13) -> filter{2,#}(x12,x13)
      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)
      app#(filtersub2(x19,x20),x21) -> filtersub{3,#}(x19,x20,x21)
     TRS:
      neq2(00(),00()) -> false0()
      neq2(00(),s1(y)) -> true0()
      neq2(s1(x),00()) -> true0()
      neq2(s1(x),s1(y)) -> neq2(x,y)
      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)
      nonzero0() -> filter1(neq1(00()))
      app(neq1(x4),x5) -> neq2(x4,x5)
      app(neq0(),x4) -> neq1(x4)
      app(s0(),x9) -> s1(x9)
      app(filter1(x12),x13) -> filter2(x12,x13)
      app(filter0(),x12) -> filter1(x12)
      app(cons1(x16),x17) -> cons2(x16,x17)
      app(cons0(),x16) -> cons1(x16)
      app(filtersub2(x19,x20),x21) -> filtersub3(x19,x20,x21)
      app(filtersub1(x19),x20) -> filtersub2(x19,x20)
      app(filtersub0(),x19) -> filtersub1(x19)
     Subterm Criterion Processor:
      simple projection:
       pi(filter{2,#}) = 0
       pi(app#) = 0
       pi(filtersub{3,#}) = 1
      problem:
       DPs:
        filtersub{3,#}(true0(),f,cons2(y,ys)) -> filter{2,#}(f,ys)
        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)
       TRS:
        neq2(00(),00()) -> false0()
        neq2(00(),s1(y)) -> true0()
        neq2(s1(x),00()) -> true0()
        neq2(s1(x),s1(y)) -> neq2(x,y)
        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)
        nonzero0() -> filter1(neq1(00()))
        app(neq1(x4),x5) -> neq2(x4,x5)
        app(neq0(),x4) -> neq1(x4)
        app(s0(),x9) -> s1(x9)
        app(filter1(x12),x13) -> filter2(x12,x13)
        app(filter0(),x12) -> filter1(x12)
        app(cons1(x16),x17) -> cons2(x16,x17)
        app(cons0(),x16) -> cons1(x16)
        app(filtersub2(x19,x20),x21) -> filtersub3(x19,x20,x21)
        app(filtersub1(x19),x20) -> filtersub2(x19,x20)
        app(filtersub0(),x19) -> filtersub1(x19)
      SCC Processor:
       #sccs: 1
       #rules: 3
       #arcs: 12/16
       DPs:
        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,#}(false0(),f,cons2(y,ys)) -> filter{2,#}(f,ys)
       TRS:
        neq2(00(),00()) -> false0()
        neq2(00(),s1(y)) -> true0()
        neq2(s1(x),00()) -> true0()
        neq2(s1(x),s1(y)) -> neq2(x,y)
        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)
        nonzero0() -> filter1(neq1(00()))
        app(neq1(x4),x5) -> neq2(x4,x5)
        app(neq0(),x4) -> neq1(x4)
        app(s0(),x9) -> s1(x9)
        app(filter1(x12),x13) -> filter2(x12,x13)
        app(filter0(),x12) -> filter1(x12)
        app(cons1(x16),x17) -> cons2(x16,x17)
        app(cons0(),x16) -> cons1(x16)
        app(filtersub2(x19,x20),x21) -> filtersub3(x19,x20,x21)
        app(filtersub1(x19),x20) -> filtersub2(x19,x20)
        app(filtersub0(),x19) -> filtersub1(x19)
       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:
          neq2(00(),00()) -> false0()
          neq2(00(),s1(y)) -> true0()
          neq2(s1(x),00()) -> true0()
          neq2(s1(x),s1(y)) -> neq2(x,y)
          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)
          nonzero0() -> filter1(neq1(00()))
          app(neq1(x4),x5) -> neq2(x4,x5)
          app(neq0(),x4) -> neq1(x4)
          app(s0(),x9) -> s1(x9)
          app(filter1(x12),x13) -> filter2(x12,x13)
          app(filter0(),x12) -> filter1(x12)
          app(cons1(x16),x17) -> cons2(x16,x17)
          app(cons0(),x16) -> cons1(x16)
          app(filtersub2(x19,x20),x21) -> filtersub3(x19,x20,x21)
          app(filtersub1(x19),x20) -> filtersub2(x19,x20)
          app(filtersub0(),x19) -> filtersub1(x19)
        SCC Processor:
         #sccs: 0
         #rules: 0
         #arcs: 4/1
         
     
     DPs:
      neq{2,#}(s1(x),s1(y)) -> neq{2,#}(x,y)
     TRS:
      neq2(00(),00()) -> false0()
      neq2(00(),s1(y)) -> true0()
      neq2(s1(x),00()) -> true0()
      neq2(s1(x),s1(y)) -> neq2(x,y)
      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)
      nonzero0() -> filter1(neq1(00()))
      app(neq1(x4),x5) -> neq2(x4,x5)
      app(neq0(),x4) -> neq1(x4)
      app(s0(),x9) -> s1(x9)
      app(filter1(x12),x13) -> filter2(x12,x13)
      app(filter0(),x12) -> filter1(x12)
      app(cons1(x16),x17) -> cons2(x16,x17)
      app(cons0(),x16) -> cons1(x16)
      app(filtersub2(x19,x20),x21) -> filtersub3(x19,x20,x21)
      app(filtersub1(x19),x20) -> filtersub2(x19,x20)
      app(filtersub0(),x19) -> filtersub1(x19)
     Subterm Criterion Processor:
      simple projection:
       pi(neq{2,#}) = 0
      problem:
       DPs:
        
       TRS:
        neq2(00(),00()) -> false0()
        neq2(00(),s1(y)) -> true0()
        neq2(s1(x),00()) -> true0()
        neq2(s1(x),s1(y)) -> neq2(x,y)
        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)
        nonzero0() -> filter1(neq1(00()))
        app(neq1(x4),x5) -> neq2(x4,x5)
        app(neq0(),x4) -> neq1(x4)
        app(s0(),x9) -> s1(x9)
        app(filter1(x12),x13) -> filter2(x12,x13)
        app(filter0(),x12) -> filter1(x12)
        app(cons1(x16),x17) -> cons2(x16,x17)
        app(cons0(),x16) -> cons1(x16)
        app(filtersub2(x19,x20),x21) -> filtersub3(x19,x20,x21)
        app(filtersub1(x19),x20) -> filtersub2(x19,x20)
        app(filtersub0(),x19) -> filtersub1(x19)
      Qed