/export/starexec/sandbox/solver/bin/starexec_run_ttt2 /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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YES

Problem:
 app(app(and(),true()),true()) -> true()
 app(app(and(),true()),false()) -> false()
 app(app(and(),false()),true()) -> false()
 app(app(and(),false()),false()) -> false()
 app(app(or(),true()),true()) -> true()
 app(app(or(),true()),false()) -> true()
 app(app(or(),false()),true()) -> true()
 app(app(or(),false()),false()) -> false()
 app(app(forall(),p),nil()) -> true()
 app(app(forall(),p),app(app(cons(),x),xs)) -> app(app(and(),app(p,x)),app(app(forall(),p),xs))
 app(app(forsome(),p),nil()) -> false()
 app(app(forsome(),p),app(app(cons(),x),xs)) -> app(app(or(),app(p,x)),app(app(forsome(),p),xs))

Proof:
 Extended Uncurrying Processor:
  application symbol: app
  symbol table:
   forsome ==> forsome0/0 forsome1/1 forsome2/2
   cons ==> cons0/0 cons1/1 cons2/2
   nil ==> nil0/0
   forall ==> forall0/0 forall1/1 forall2/2
   or ==> or0/0 or1/1 or2/2
   false ==> false0/0
   true ==> true0/0
   and ==> and0/0 and1/1 and2/2
   
  uncurry-rules:
   app(and1(x3),x4) -> and2(x3,x4)
   app(and0(),x3) -> and1(x3)
   app(or1(x8),x9) -> or2(x8,x9)
   app(or0(),x8) -> or1(x8)
   app(forall1(x11),x12) -> forall2(x11,x12)
   app(forall0(),x11) -> forall1(x11)
   app(cons1(x15),x16) -> cons2(x15,x16)
   app(cons0(),x15) -> cons1(x15)
   app(forsome1(x18),x19) -> forsome2(x18,x19)
   app(forsome0(),x18) -> forsome1(x18)
  eta-rules:
   
  problem:
   and2(true0(),true0()) -> true0()
   and2(true0(),false0()) -> false0()
   and2(false0(),true0()) -> false0()
   and2(false0(),false0()) -> false0()
   or2(true0(),true0()) -> true0()
   or2(true0(),false0()) -> true0()
   or2(false0(),true0()) -> true0()
   or2(false0(),false0()) -> false0()
   forall2(p,nil0()) -> true0()
   forall2(p,cons2(x,xs)) -> and2(app(p,x),forall2(p,xs))
   forsome2(p,nil0()) -> false0()
   forsome2(p,cons2(x,xs)) -> or2(app(p,x),forsome2(p,xs))
   app(and1(x3),x4) -> and2(x3,x4)
   app(and0(),x3) -> and1(x3)
   app(or1(x8),x9) -> or2(x8,x9)
   app(or0(),x8) -> or1(x8)
   app(forall1(x11),x12) -> forall2(x11,x12)
   app(forall0(),x11) -> forall1(x11)
   app(cons1(x15),x16) -> cons2(x15,x16)
   app(cons0(),x15) -> cons1(x15)
   app(forsome1(x18),x19) -> forsome2(x18,x19)
   app(forsome0(),x18) -> forsome1(x18)
  DP Processor:
   DPs:
    forall{2,#}(p,cons2(x,xs)) -> forall{2,#}(p,xs)
    forall{2,#}(p,cons2(x,xs)) -> app#(p,x)
    forall{2,#}(p,cons2(x,xs)) -> and{2,#}(app(p,x),forall2(p,xs))
    forsome{2,#}(p,cons2(x,xs)) -> forsome{2,#}(p,xs)
    forsome{2,#}(p,cons2(x,xs)) -> app#(p,x)
    forsome{2,#}(p,cons2(x,xs)) -> or{2,#}(app(p,x),forsome2(p,xs))
    app#(and1(x3),x4) -> and{2,#}(x3,x4)
    app#(or1(x8),x9) -> or{2,#}(x8,x9)
    app#(forall1(x11),x12) -> forall{2,#}(x11,x12)
    app#(forsome1(x18),x19) -> forsome{2,#}(x18,x19)
   TRS:
    and2(true0(),true0()) -> true0()
    and2(true0(),false0()) -> false0()
    and2(false0(),true0()) -> false0()
    and2(false0(),false0()) -> false0()
    or2(true0(),true0()) -> true0()
    or2(true0(),false0()) -> true0()
    or2(false0(),true0()) -> true0()
    or2(false0(),false0()) -> false0()
    forall2(p,nil0()) -> true0()
    forall2(p,cons2(x,xs)) -> and2(app(p,x),forall2(p,xs))
    forsome2(p,nil0()) -> false0()
    forsome2(p,cons2(x,xs)) -> or2(app(p,x),forsome2(p,xs))
    app(and1(x3),x4) -> and2(x3,x4)
    app(and0(),x3) -> and1(x3)
    app(or1(x8),x9) -> or2(x8,x9)
    app(or0(),x8) -> or1(x8)
    app(forall1(x11),x12) -> forall2(x11,x12)
    app(forall0(),x11) -> forall1(x11)
    app(cons1(x15),x16) -> cons2(x15,x16)
    app(cons0(),x15) -> cons1(x15)
    app(forsome1(x18),x19) -> forsome2(x18,x19)
    app(forsome0(),x18) -> forsome1(x18)
   TDG Processor:
    DPs:
     forall{2,#}(p,cons2(x,xs)) -> forall{2,#}(p,xs)
     forall{2,#}(p,cons2(x,xs)) -> app#(p,x)
     forall{2,#}(p,cons2(x,xs)) -> and{2,#}(app(p,x),forall2(p,xs))
     forsome{2,#}(p,cons2(x,xs)) -> forsome{2,#}(p,xs)
     forsome{2,#}(p,cons2(x,xs)) -> app#(p,x)
     forsome{2,#}(p,cons2(x,xs)) -> or{2,#}(app(p,x),forsome2(p,xs))
     app#(and1(x3),x4) -> and{2,#}(x3,x4)
     app#(or1(x8),x9) -> or{2,#}(x8,x9)
     app#(forall1(x11),x12) -> forall{2,#}(x11,x12)
     app#(forsome1(x18),x19) -> forsome{2,#}(x18,x19)
    TRS:
     and2(true0(),true0()) -> true0()
     and2(true0(),false0()) -> false0()
     and2(false0(),true0()) -> false0()
     and2(false0(),false0()) -> false0()
     or2(true0(),true0()) -> true0()
     or2(true0(),false0()) -> true0()
     or2(false0(),true0()) -> true0()
     or2(false0(),false0()) -> false0()
     forall2(p,nil0()) -> true0()
     forall2(p,cons2(x,xs)) -> and2(app(p,x),forall2(p,xs))
     forsome2(p,nil0()) -> false0()
     forsome2(p,cons2(x,xs)) -> or2(app(p,x),forsome2(p,xs))
     app(and1(x3),x4) -> and2(x3,x4)
     app(and0(),x3) -> and1(x3)
     app(or1(x8),x9) -> or2(x8,x9)
     app(or0(),x8) -> or1(x8)
     app(forall1(x11),x12) -> forall2(x11,x12)
     app(forall0(),x11) -> forall1(x11)
     app(cons1(x15),x16) -> cons2(x15,x16)
     app(cons0(),x15) -> cons1(x15)
     app(forsome1(x18),x19) -> forsome2(x18,x19)
     app(forsome0(),x18) -> forsome1(x18)
    graph:
     forsome{2,#}(p,cons2(x,xs)) -> forsome{2,#}(p,xs) ->
     forsome{2,#}(p,cons2(x,xs)) -> or{2,#}(app(p,x),forsome2(p,xs))
     forsome{2,#}(p,cons2(x,xs)) -> forsome{2,#}(p,xs) ->
     forsome{2,#}(p,cons2(x,xs)) -> app#(p,x)
     forsome{2,#}(p,cons2(x,xs)) -> forsome{2,#}(p,xs) ->
     forsome{2,#}(p,cons2(x,xs)) -> forsome{2,#}(p,xs)
     forsome{2,#}(p,cons2(x,xs)) -> app#(p,x) ->
     app#(forsome1(x18),x19) -> forsome{2,#}(x18,x19)
     forsome{2,#}(p,cons2(x,xs)) -> app#(p,x) ->
     app#(forall1(x11),x12) -> forall{2,#}(x11,x12)
     forsome{2,#}(p,cons2(x,xs)) -> app#(p,x) ->
     app#(or1(x8),x9) -> or{2,#}(x8,x9)
     forsome{2,#}(p,cons2(x,xs)) -> app#(p,x) ->
     app#(and1(x3),x4) -> and{2,#}(x3,x4)
     app#(forsome1(x18),x19) -> forsome{2,#}(x18,x19) ->
     forsome{2,#}(p,cons2(x,xs)) -> or{2,#}(app(p,x),forsome2(p,xs))
     app#(forsome1(x18),x19) -> forsome{2,#}(x18,x19) ->
     forsome{2,#}(p,cons2(x,xs)) -> app#(p,x)
     app#(forsome1(x18),x19) -> forsome{2,#}(x18,x19) ->
     forsome{2,#}(p,cons2(x,xs)) -> forsome{2,#}(p,xs)
     app#(forall1(x11),x12) -> forall{2,#}(x11,x12) ->
     forall{2,#}(p,cons2(x,xs)) -> and{2,#}(app(p,x),forall2(p,xs))
     app#(forall1(x11),x12) -> forall{2,#}(x11,x12) ->
     forall{2,#}(p,cons2(x,xs)) -> app#(p,x)
     app#(forall1(x11),x12) -> forall{2,#}(x11,x12) ->
     forall{2,#}(p,cons2(x,xs)) -> forall{2,#}(p,xs)
     forall{2,#}(p,cons2(x,xs)) -> app#(p,x) ->
     app#(forsome1(x18),x19) -> forsome{2,#}(x18,x19)
     forall{2,#}(p,cons2(x,xs)) -> app#(p,x) ->
     app#(forall1(x11),x12) -> forall{2,#}(x11,x12)
     forall{2,#}(p,cons2(x,xs)) -> app#(p,x) ->
     app#(or1(x8),x9) -> or{2,#}(x8,x9)
     forall{2,#}(p,cons2(x,xs)) -> app#(p,x) ->
     app#(and1(x3),x4) -> and{2,#}(x3,x4)
     forall{2,#}(p,cons2(x,xs)) -> forall{2,#}(p,xs) ->
     forall{2,#}(p,cons2(x,xs)) -> and{2,#}(app(p,x),forall2(p,xs))
     forall{2,#}(p,cons2(x,xs)) -> forall{2,#}(p,xs) ->
     forall{2,#}(p,cons2(x,xs)) -> app#(p,x)
     forall{2,#}(p,cons2(x,xs)) -> forall{2,#}(p,xs) ->
     forall{2,#}(p,cons2(x,xs)) -> forall{2,#}(p,xs)
    SCC Processor:
     #sccs: 1
     #rules: 6
     #arcs: 20/100
     DPs:
      forsome{2,#}(p,cons2(x,xs)) -> forsome{2,#}(p,xs)
      forsome{2,#}(p,cons2(x,xs)) -> app#(p,x)
      app#(forall1(x11),x12) -> forall{2,#}(x11,x12)
      forall{2,#}(p,cons2(x,xs)) -> forall{2,#}(p,xs)
      forall{2,#}(p,cons2(x,xs)) -> app#(p,x)
      app#(forsome1(x18),x19) -> forsome{2,#}(x18,x19)
     TRS:
      and2(true0(),true0()) -> true0()
      and2(true0(),false0()) -> false0()
      and2(false0(),true0()) -> false0()
      and2(false0(),false0()) -> false0()
      or2(true0(),true0()) -> true0()
      or2(true0(),false0()) -> true0()
      or2(false0(),true0()) -> true0()
      or2(false0(),false0()) -> false0()
      forall2(p,nil0()) -> true0()
      forall2(p,cons2(x,xs)) -> and2(app(p,x),forall2(p,xs))
      forsome2(p,nil0()) -> false0()
      forsome2(p,cons2(x,xs)) -> or2(app(p,x),forsome2(p,xs))
      app(and1(x3),x4) -> and2(x3,x4)
      app(and0(),x3) -> and1(x3)
      app(or1(x8),x9) -> or2(x8,x9)
      app(or0(),x8) -> or1(x8)
      app(forall1(x11),x12) -> forall2(x11,x12)
      app(forall0(),x11) -> forall1(x11)
      app(cons1(x15),x16) -> cons2(x15,x16)
      app(cons0(),x15) -> cons1(x15)
      app(forsome1(x18),x19) -> forsome2(x18,x19)
      app(forsome0(),x18) -> forsome1(x18)
     Subterm Criterion Processor:
      simple projection:
       pi(forall{2,#}) = 0
       pi(app#) = 0
       pi(forsome{2,#}) = 0
      problem:
       DPs:
        forsome{2,#}(p,cons2(x,xs)) -> forsome{2,#}(p,xs)
        forsome{2,#}(p,cons2(x,xs)) -> app#(p,x)
        forall{2,#}(p,cons2(x,xs)) -> forall{2,#}(p,xs)
        forall{2,#}(p,cons2(x,xs)) -> app#(p,x)
       TRS:
        and2(true0(),true0()) -> true0()
        and2(true0(),false0()) -> false0()
        and2(false0(),true0()) -> false0()
        and2(false0(),false0()) -> false0()
        or2(true0(),true0()) -> true0()
        or2(true0(),false0()) -> true0()
        or2(false0(),true0()) -> true0()
        or2(false0(),false0()) -> false0()
        forall2(p,nil0()) -> true0()
        forall2(p,cons2(x,xs)) -> and2(app(p,x),forall2(p,xs))
        forsome2(p,nil0()) -> false0()
        forsome2(p,cons2(x,xs)) -> or2(app(p,x),forsome2(p,xs))
        app(and1(x3),x4) -> and2(x3,x4)
        app(and0(),x3) -> and1(x3)
        app(or1(x8),x9) -> or2(x8,x9)
        app(or0(),x8) -> or1(x8)
        app(forall1(x11),x12) -> forall2(x11,x12)
        app(forall0(),x11) -> forall1(x11)
        app(cons1(x15),x16) -> cons2(x15,x16)
        app(cons0(),x15) -> cons1(x15)
        app(forsome1(x18),x19) -> forsome2(x18,x19)
        app(forsome0(),x18) -> forsome1(x18)
      SCC Processor:
       #sccs: 2
       #rules: 2
       #arcs: 12/16
       DPs:
        forall{2,#}(p,cons2(x,xs)) -> forall{2,#}(p,xs)
       TRS:
        and2(true0(),true0()) -> true0()
        and2(true0(),false0()) -> false0()
        and2(false0(),true0()) -> false0()
        and2(false0(),false0()) -> false0()
        or2(true0(),true0()) -> true0()
        or2(true0(),false0()) -> true0()
        or2(false0(),true0()) -> true0()
        or2(false0(),false0()) -> false0()
        forall2(p,nil0()) -> true0()
        forall2(p,cons2(x,xs)) -> and2(app(p,x),forall2(p,xs))
        forsome2(p,nil0()) -> false0()
        forsome2(p,cons2(x,xs)) -> or2(app(p,x),forsome2(p,xs))
        app(and1(x3),x4) -> and2(x3,x4)
        app(and0(),x3) -> and1(x3)
        app(or1(x8),x9) -> or2(x8,x9)
        app(or0(),x8) -> or1(x8)
        app(forall1(x11),x12) -> forall2(x11,x12)
        app(forall0(),x11) -> forall1(x11)
        app(cons1(x15),x16) -> cons2(x15,x16)
        app(cons0(),x15) -> cons1(x15)
        app(forsome1(x18),x19) -> forsome2(x18,x19)
        app(forsome0(),x18) -> forsome1(x18)
       Subterm Criterion Processor:
        simple projection:
         pi(forall{2,#}) = 1
        problem:
         DPs:
          
         TRS:
          and2(true0(),true0()) -> true0()
          and2(true0(),false0()) -> false0()
          and2(false0(),true0()) -> false0()
          and2(false0(),false0()) -> false0()
          or2(true0(),true0()) -> true0()
          or2(true0(),false0()) -> true0()
          or2(false0(),true0()) -> true0()
          or2(false0(),false0()) -> false0()
          forall2(p,nil0()) -> true0()
          forall2(p,cons2(x,xs)) -> and2(app(p,x),forall2(p,xs))
          forsome2(p,nil0()) -> false0()
          forsome2(p,cons2(x,xs)) -> or2(app(p,x),forsome2(p,xs))
          app(and1(x3),x4) -> and2(x3,x4)
          app(and0(),x3) -> and1(x3)
          app(or1(x8),x9) -> or2(x8,x9)
          app(or0(),x8) -> or1(x8)
          app(forall1(x11),x12) -> forall2(x11,x12)
          app(forall0(),x11) -> forall1(x11)
          app(cons1(x15),x16) -> cons2(x15,x16)
          app(cons0(),x15) -> cons1(x15)
          app(forsome1(x18),x19) -> forsome2(x18,x19)
          app(forsome0(),x18) -> forsome1(x18)
        Qed
       
       DPs:
        forsome{2,#}(p,cons2(x,xs)) -> forsome{2,#}(p,xs)
       TRS:
        and2(true0(),true0()) -> true0()
        and2(true0(),false0()) -> false0()
        and2(false0(),true0()) -> false0()
        and2(false0(),false0()) -> false0()
        or2(true0(),true0()) -> true0()
        or2(true0(),false0()) -> true0()
        or2(false0(),true0()) -> true0()
        or2(false0(),false0()) -> false0()
        forall2(p,nil0()) -> true0()
        forall2(p,cons2(x,xs)) -> and2(app(p,x),forall2(p,xs))
        forsome2(p,nil0()) -> false0()
        forsome2(p,cons2(x,xs)) -> or2(app(p,x),forsome2(p,xs))
        app(and1(x3),x4) -> and2(x3,x4)
        app(and0(),x3) -> and1(x3)
        app(or1(x8),x9) -> or2(x8,x9)
        app(or0(),x8) -> or1(x8)
        app(forall1(x11),x12) -> forall2(x11,x12)
        app(forall0(),x11) -> forall1(x11)
        app(cons1(x15),x16) -> cons2(x15,x16)
        app(cons0(),x15) -> cons1(x15)
        app(forsome1(x18),x19) -> forsome2(x18,x19)
        app(forsome0(),x18) -> forsome1(x18)
       Subterm Criterion Processor:
        simple projection:
         pi(forsome{2,#}) = 1
        problem:
         DPs:
          
         TRS:
          and2(true0(),true0()) -> true0()
          and2(true0(),false0()) -> false0()
          and2(false0(),true0()) -> false0()
          and2(false0(),false0()) -> false0()
          or2(true0(),true0()) -> true0()
          or2(true0(),false0()) -> true0()
          or2(false0(),true0()) -> true0()
          or2(false0(),false0()) -> false0()
          forall2(p,nil0()) -> true0()
          forall2(p,cons2(x,xs)) -> and2(app(p,x),forall2(p,xs))
          forsome2(p,nil0()) -> false0()
          forsome2(p,cons2(x,xs)) -> or2(app(p,x),forsome2(p,xs))
          app(and1(x3),x4) -> and2(x3,x4)
          app(and0(),x3) -> and1(x3)
          app(or1(x8),x9) -> or2(x8,x9)
          app(or0(),x8) -> or1(x8)
          app(forall1(x11),x12) -> forall2(x11,x12)
          app(forall0(),x11) -> forall1(x11)
          app(cons1(x15),x16) -> cons2(x15,x16)
          app(cons0(),x15) -> cons1(x15)
          app(forsome1(x18),x19) -> forsome2(x18,x19)
          app(forsome0(),x18) -> forsome1(x18)
        Qed