/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(lt(),app(s(),x)),app(s(),y)) -> app(app(lt(),x),y)
 app(app(lt(),0()),app(s(),y)) -> true()
 app(app(lt(),y),0()) -> false()
 app(app(eq(),x),x) -> true()
 app(app(eq(),app(s(),x)),0()) -> false()
 app(app(eq(),0()),app(s(),x)) -> false()
 app(app(member(),w),null()) -> false()
 app(app(member(),w),app(app(app(fork(),x),y),z)) ->
 app(app(app(if(),app(app(lt(),w),y)),app(app(member(),w),x)),app(app
                                                                  (app(if(),app(app(eq(),w),y)),
                                                                   true
                                                                   ()),
                                                                  app(app(member(),w),z)))

Proof:
 Extended Uncurrying Processor:
  application symbol: app
  symbol table:
   if ==> if0/0 if1/1 if2/2 if3/3
   fork ==> fork0/0 fork1/1 fork2/2 fork3/3
   null ==> null0/0
   member ==> member0/0 member1/1 member2/2
   eq ==> eq0/0 eq1/1 eq2/2
   false ==> false0/0
   true ==> true0/0
   0 ==> 00/0
   s ==> s0/0 s1/1
   lt ==> lt0/0 lt1/1 lt2/2
   
  uncurry-rules:
   app(lt1(x4),x5) -> lt2(x4,x5)
   app(lt0(),x4) -> lt1(x4)
   app(s0(),x7) -> s1(x7)
   app(eq1(x12),x13) -> eq2(x12,x13)
   app(eq0(),x12) -> eq1(x12)
   app(member1(x15),x16) -> member2(x15,x16)
   app(member0(),x15) -> member1(x15)
   app(fork2(x19,x20),x21) -> fork3(x19,x20,x21)
   app(fork1(x19),x20) -> fork2(x19,x20)
   app(fork0(),x19) -> fork1(x19)
   app(if2(x23,x24),x25) -> if3(x23,x24,x25)
   app(if1(x23),x24) -> if2(x23,x24)
   app(if0(),x23) -> if1(x23)
  eta-rules:
   
  problem:
   lt2(s1(x),s1(y)) -> lt2(x,y)
   lt2(00(),s1(y)) -> true0()
   lt2(y,00()) -> false0()
   eq2(x,x) -> true0()
   eq2(s1(x),00()) -> false0()
   eq2(00(),s1(x)) -> false0()
   member2(w,null0()) -> false0()
   member2(w,fork3(x,y,z)) -> if3(lt2(w,y),member2(w,x),if3(eq2(w,y),true0(),member2(w,z)))
   app(lt1(x4),x5) -> lt2(x4,x5)
   app(lt0(),x4) -> lt1(x4)
   app(s0(),x7) -> s1(x7)
   app(eq1(x12),x13) -> eq2(x12,x13)
   app(eq0(),x12) -> eq1(x12)
   app(member1(x15),x16) -> member2(x15,x16)
   app(member0(),x15) -> member1(x15)
   app(fork2(x19,x20),x21) -> fork3(x19,x20,x21)
   app(fork1(x19),x20) -> fork2(x19,x20)
   app(fork0(),x19) -> fork1(x19)
   app(if2(x23,x24),x25) -> if3(x23,x24,x25)
   app(if1(x23),x24) -> if2(x23,x24)
   app(if0(),x23) -> if1(x23)
  DP Processor:
   DPs:
    lt{2,#}(s1(x),s1(y)) -> lt{2,#}(x,y)
    member{2,#}(w,fork3(x,y,z)) -> member{2,#}(w,z)
    member{2,#}(w,fork3(x,y,z)) -> eq{2,#}(w,y)
    member{2,#}(w,fork3(x,y,z)) -> member{2,#}(w,x)
    member{2,#}(w,fork3(x,y,z)) -> lt{2,#}(w,y)
    app#(lt1(x4),x5) -> lt{2,#}(x4,x5)
    app#(eq1(x12),x13) -> eq{2,#}(x12,x13)
    app#(member1(x15),x16) -> member{2,#}(x15,x16)
   TRS:
    lt2(s1(x),s1(y)) -> lt2(x,y)
    lt2(00(),s1(y)) -> true0()
    lt2(y,00()) -> false0()
    eq2(x,x) -> true0()
    eq2(s1(x),00()) -> false0()
    eq2(00(),s1(x)) -> false0()
    member2(w,null0()) -> false0()
    member2(w,fork3(x,y,z)) -> if3(lt2(w,y),member2(w,x),if3(eq2(w,y),true0(),member2(w,z)))
    app(lt1(x4),x5) -> lt2(x4,x5)
    app(lt0(),x4) -> lt1(x4)
    app(s0(),x7) -> s1(x7)
    app(eq1(x12),x13) -> eq2(x12,x13)
    app(eq0(),x12) -> eq1(x12)
    app(member1(x15),x16) -> member2(x15,x16)
    app(member0(),x15) -> member1(x15)
    app(fork2(x19,x20),x21) -> fork3(x19,x20,x21)
    app(fork1(x19),x20) -> fork2(x19,x20)
    app(fork0(),x19) -> fork1(x19)
    app(if2(x23,x24),x25) -> if3(x23,x24,x25)
    app(if1(x23),x24) -> if2(x23,x24)
    app(if0(),x23) -> if1(x23)
   TDG Processor:
    DPs:
     lt{2,#}(s1(x),s1(y)) -> lt{2,#}(x,y)
     member{2,#}(w,fork3(x,y,z)) -> member{2,#}(w,z)
     member{2,#}(w,fork3(x,y,z)) -> eq{2,#}(w,y)
     member{2,#}(w,fork3(x,y,z)) -> member{2,#}(w,x)
     member{2,#}(w,fork3(x,y,z)) -> lt{2,#}(w,y)
     app#(lt1(x4),x5) -> lt{2,#}(x4,x5)
     app#(eq1(x12),x13) -> eq{2,#}(x12,x13)
     app#(member1(x15),x16) -> member{2,#}(x15,x16)
    TRS:
     lt2(s1(x),s1(y)) -> lt2(x,y)
     lt2(00(),s1(y)) -> true0()
     lt2(y,00()) -> false0()
     eq2(x,x) -> true0()
     eq2(s1(x),00()) -> false0()
     eq2(00(),s1(x)) -> false0()
     member2(w,null0()) -> false0()
     member2(w,fork3(x,y,z)) -> if3(lt2(w,y),member2(w,x),if3(eq2(w,y),true0(),member2(w,z)))
     app(lt1(x4),x5) -> lt2(x4,x5)
     app(lt0(),x4) -> lt1(x4)
     app(s0(),x7) -> s1(x7)
     app(eq1(x12),x13) -> eq2(x12,x13)
     app(eq0(),x12) -> eq1(x12)
     app(member1(x15),x16) -> member2(x15,x16)
     app(member0(),x15) -> member1(x15)
     app(fork2(x19,x20),x21) -> fork3(x19,x20,x21)
     app(fork1(x19),x20) -> fork2(x19,x20)
     app(fork0(),x19) -> fork1(x19)
     app(if2(x23,x24),x25) -> if3(x23,x24,x25)
     app(if1(x23),x24) -> if2(x23,x24)
     app(if0(),x23) -> if1(x23)
    graph:
     app#(member1(x15),x16) -> member{2,#}(x15,x16) ->
     member{2,#}(w,fork3(x,y,z)) -> lt{2,#}(w,y)
     app#(member1(x15),x16) -> member{2,#}(x15,x16) ->
     member{2,#}(w,fork3(x,y,z)) -> member{2,#}(w,x)
     app#(member1(x15),x16) -> member{2,#}(x15,x16) ->
     member{2,#}(w,fork3(x,y,z)) -> eq{2,#}(w,y)
     app#(member1(x15),x16) -> member{2,#}(x15,x16) ->
     member{2,#}(w,fork3(x,y,z)) -> member{2,#}(w,z)
     app#(lt1(x4),x5) -> lt{2,#}(x4,x5) ->
     lt{2,#}(s1(x),s1(y)) -> lt{2,#}(x,y)
     member{2,#}(w,fork3(x,y,z)) -> member{2,#}(w,z) ->
     member{2,#}(w,fork3(x,y,z)) -> lt{2,#}(w,y)
     member{2,#}(w,fork3(x,y,z)) -> member{2,#}(w,z) ->
     member{2,#}(w,fork3(x,y,z)) -> member{2,#}(w,x)
     member{2,#}(w,fork3(x,y,z)) -> member{2,#}(w,z) ->
     member{2,#}(w,fork3(x,y,z)) -> eq{2,#}(w,y)
     member{2,#}(w,fork3(x,y,z)) -> member{2,#}(w,z) ->
     member{2,#}(w,fork3(x,y,z)) -> member{2,#}(w,z)
     member{2,#}(w,fork3(x,y,z)) -> member{2,#}(w,x) ->
     member{2,#}(w,fork3(x,y,z)) -> lt{2,#}(w,y)
     member{2,#}(w,fork3(x,y,z)) -> member{2,#}(w,x) ->
     member{2,#}(w,fork3(x,y,z)) -> member{2,#}(w,x)
     member{2,#}(w,fork3(x,y,z)) -> member{2,#}(w,x) ->
     member{2,#}(w,fork3(x,y,z)) -> eq{2,#}(w,y)
     member{2,#}(w,fork3(x,y,z)) -> member{2,#}(w,x) ->
     member{2,#}(w,fork3(x,y,z)) -> member{2,#}(w,z)
     member{2,#}(w,fork3(x,y,z)) -> lt{2,#}(w,y) ->
     lt{2,#}(s1(x),s1(y)) -> lt{2,#}(x,y)
     lt{2,#}(s1(x),s1(y)) -> lt{2,#}(x,y) -> lt{2,#}(s1(x),s1(y)) -> lt{2,#}(x,y)
    SCC Processor:
     #sccs: 2
     #rules: 3
     #arcs: 15/64
     DPs:
      member{2,#}(w,fork3(x,y,z)) -> member{2,#}(w,z)
      member{2,#}(w,fork3(x,y,z)) -> member{2,#}(w,x)
     TRS:
      lt2(s1(x),s1(y)) -> lt2(x,y)
      lt2(00(),s1(y)) -> true0()
      lt2(y,00()) -> false0()
      eq2(x,x) -> true0()
      eq2(s1(x),00()) -> false0()
      eq2(00(),s1(x)) -> false0()
      member2(w,null0()) -> false0()
      member2(w,fork3(x,y,z)) -> if3(lt2(w,y),member2(w,x),if3(eq2(w,y),true0(),member2(w,z)))
      app(lt1(x4),x5) -> lt2(x4,x5)
      app(lt0(),x4) -> lt1(x4)
      app(s0(),x7) -> s1(x7)
      app(eq1(x12),x13) -> eq2(x12,x13)
      app(eq0(),x12) -> eq1(x12)
      app(member1(x15),x16) -> member2(x15,x16)
      app(member0(),x15) -> member1(x15)
      app(fork2(x19,x20),x21) -> fork3(x19,x20,x21)
      app(fork1(x19),x20) -> fork2(x19,x20)
      app(fork0(),x19) -> fork1(x19)
      app(if2(x23,x24),x25) -> if3(x23,x24,x25)
      app(if1(x23),x24) -> if2(x23,x24)
      app(if0(),x23) -> if1(x23)
     Subterm Criterion Processor:
      simple projection:
       pi(member{2,#}) = 1
      problem:
       DPs:
        
       TRS:
        lt2(s1(x),s1(y)) -> lt2(x,y)
        lt2(00(),s1(y)) -> true0()
        lt2(y,00()) -> false0()
        eq2(x,x) -> true0()
        eq2(s1(x),00()) -> false0()
        eq2(00(),s1(x)) -> false0()
        member2(w,null0()) -> false0()
        member2(w,fork3(x,y,z)) -> if3(lt2(w,y),member2(w,x),if3(eq2(w,y),true0(),member2(w,z)))
        app(lt1(x4),x5) -> lt2(x4,x5)
        app(lt0(),x4) -> lt1(x4)
        app(s0(),x7) -> s1(x7)
        app(eq1(x12),x13) -> eq2(x12,x13)
        app(eq0(),x12) -> eq1(x12)
        app(member1(x15),x16) -> member2(x15,x16)
        app(member0(),x15) -> member1(x15)
        app(fork2(x19,x20),x21) -> fork3(x19,x20,x21)
        app(fork1(x19),x20) -> fork2(x19,x20)
        app(fork0(),x19) -> fork1(x19)
        app(if2(x23,x24),x25) -> if3(x23,x24,x25)
        app(if1(x23),x24) -> if2(x23,x24)
        app(if0(),x23) -> if1(x23)
      Qed
     
     DPs:
      lt{2,#}(s1(x),s1(y)) -> lt{2,#}(x,y)
     TRS:
      lt2(s1(x),s1(y)) -> lt2(x,y)
      lt2(00(),s1(y)) -> true0()
      lt2(y,00()) -> false0()
      eq2(x,x) -> true0()
      eq2(s1(x),00()) -> false0()
      eq2(00(),s1(x)) -> false0()
      member2(w,null0()) -> false0()
      member2(w,fork3(x,y,z)) -> if3(lt2(w,y),member2(w,x),if3(eq2(w,y),true0(),member2(w,z)))
      app(lt1(x4),x5) -> lt2(x4,x5)
      app(lt0(),x4) -> lt1(x4)
      app(s0(),x7) -> s1(x7)
      app(eq1(x12),x13) -> eq2(x12,x13)
      app(eq0(),x12) -> eq1(x12)
      app(member1(x15),x16) -> member2(x15,x16)
      app(member0(),x15) -> member1(x15)
      app(fork2(x19,x20),x21) -> fork3(x19,x20,x21)
      app(fork1(x19),x20) -> fork2(x19,x20)
      app(fork0(),x19) -> fork1(x19)
      app(if2(x23,x24),x25) -> if3(x23,x24,x25)
      app(if1(x23),x24) -> if2(x23,x24)
      app(if0(),x23) -> if1(x23)
     Subterm Criterion Processor:
      simple projection:
       pi(lt{2,#}) = 0
      problem:
       DPs:
        
       TRS:
        lt2(s1(x),s1(y)) -> lt2(x,y)
        lt2(00(),s1(y)) -> true0()
        lt2(y,00()) -> false0()
        eq2(x,x) -> true0()
        eq2(s1(x),00()) -> false0()
        eq2(00(),s1(x)) -> false0()
        member2(w,null0()) -> false0()
        member2(w,fork3(x,y,z)) -> if3(lt2(w,y),member2(w,x),if3(eq2(w,y),true0(),member2(w,z)))
        app(lt1(x4),x5) -> lt2(x4,x5)
        app(lt0(),x4) -> lt1(x4)
        app(s0(),x7) -> s1(x7)
        app(eq1(x12),x13) -> eq2(x12,x13)
        app(eq0(),x12) -> eq1(x12)
        app(member1(x15),x16) -> member2(x15,x16)
        app(member0(),x15) -> member1(x15)
        app(fork2(x19,x20),x21) -> fork3(x19,x20,x21)
        app(fork1(x19),x20) -> fork2(x19,x20)
        app(fork0(),x19) -> fork1(x19)
        app(if2(x23,x24),x25) -> if3(x23,x24,x25)
        app(if1(x23),x24) -> if2(x23,x24)
        app(if0(),x23) -> if1(x23)
      Qed