/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(and(),true()),true()) -> true()
 app(app(and(),x),false()) -> false()
 app(app(and(),false()),y) -> false()
 app(app(or(),true()),y) -> true()
 app(app(or(),x),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(x4),x5) -> and2(x4,x5)
   app(and0(),x4) -> and1(x4)
   app(or1(x9),x10) -> or2(x9,x10)
   app(or0(),x9) -> or1(x9)
   app(forall1(x12),x13) -> forall2(x12,x13)
   app(forall0(),x12) -> forall1(x12)
   app(cons1(x16),x17) -> cons2(x16,x17)
   app(cons0(),x16) -> cons1(x16)
   app(forsome1(x19),x20) -> forsome2(x19,x20)
   app(forsome0(),x19) -> forsome1(x19)
  eta-rules:
   
  problem:
   and2(true0(),true0()) -> true0()
   and2(x,false0()) -> false0()
   and2(false0(),y) -> false0()
   or2(true0(),y) -> true0()
   or2(x,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(x4),x5) -> and2(x4,x5)
   app(and0(),x4) -> and1(x4)
   app(or1(x9),x10) -> or2(x9,x10)
   app(or0(),x9) -> or1(x9)
   app(forall1(x12),x13) -> forall2(x12,x13)
   app(forall0(),x12) -> forall1(x12)
   app(cons1(x16),x17) -> cons2(x16,x17)
   app(cons0(),x16) -> cons1(x16)
   app(forsome1(x19),x20) -> forsome2(x19,x20)
   app(forsome0(),x19) -> forsome1(x19)
  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(x4),x5) -> and{2,#}(x4,x5)
    app#(or1(x9),x10) -> or{2,#}(x9,x10)
    app#(forall1(x12),x13) -> forall{2,#}(x12,x13)
    app#(forsome1(x19),x20) -> forsome{2,#}(x19,x20)
   TRS:
    and2(true0(),true0()) -> true0()
    and2(x,false0()) -> false0()
    and2(false0(),y) -> false0()
    or2(true0(),y) -> true0()
    or2(x,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(x4),x5) -> and2(x4,x5)
    app(and0(),x4) -> and1(x4)
    app(or1(x9),x10) -> or2(x9,x10)
    app(or0(),x9) -> or1(x9)
    app(forall1(x12),x13) -> forall2(x12,x13)
    app(forall0(),x12) -> forall1(x12)
    app(cons1(x16),x17) -> cons2(x16,x17)
    app(cons0(),x16) -> cons1(x16)
    app(forsome1(x19),x20) -> forsome2(x19,x20)
    app(forsome0(),x19) -> forsome1(x19)
   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(x4),x5) -> and{2,#}(x4,x5)
     app#(or1(x9),x10) -> or{2,#}(x9,x10)
     app#(forall1(x12),x13) -> forall{2,#}(x12,x13)
     app#(forsome1(x19),x20) -> forsome{2,#}(x19,x20)
    TRS:
     and2(true0(),true0()) -> true0()
     and2(x,false0()) -> false0()
     and2(false0(),y) -> false0()
     or2(true0(),y) -> true0()
     or2(x,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(x4),x5) -> and2(x4,x5)
     app(and0(),x4) -> and1(x4)
     app(or1(x9),x10) -> or2(x9,x10)
     app(or0(),x9) -> or1(x9)
     app(forall1(x12),x13) -> forall2(x12,x13)
     app(forall0(),x12) -> forall1(x12)
     app(cons1(x16),x17) -> cons2(x16,x17)
     app(cons0(),x16) -> cons1(x16)
     app(forsome1(x19),x20) -> forsome2(x19,x20)
     app(forsome0(),x19) -> forsome1(x19)
    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(x19),x20) -> forsome{2,#}(x19,x20)
     forsome{2,#}(p,cons2(x,xs)) -> app#(p,x) ->
     app#(forall1(x12),x13) -> forall{2,#}(x12,x13)
     forsome{2,#}(p,cons2(x,xs)) -> app#(p,x) ->
     app#(or1(x9),x10) -> or{2,#}(x9,x10)
     forsome{2,#}(p,cons2(x,xs)) -> app#(p,x) ->
     app#(and1(x4),x5) -> and{2,#}(x4,x5)
     app#(forsome1(x19),x20) -> forsome{2,#}(x19,x20) ->
     forsome{2,#}(p,cons2(x,xs)) -> or{2,#}(app(p,x),forsome2(p,xs))
     app#(forsome1(x19),x20) -> forsome{2,#}(x19,x20) ->
     forsome{2,#}(p,cons2(x,xs)) -> app#(p,x)
     app#(forsome1(x19),x20) -> forsome{2,#}(x19,x20) ->
     forsome{2,#}(p,cons2(x,xs)) -> forsome{2,#}(p,xs)
     app#(forall1(x12),x13) -> forall{2,#}(x12,x13) ->
     forall{2,#}(p,cons2(x,xs)) -> and{2,#}(app(p,x),forall2(p,xs))
     app#(forall1(x12),x13) -> forall{2,#}(x12,x13) ->
     forall{2,#}(p,cons2(x,xs)) -> app#(p,x)
     app#(forall1(x12),x13) -> forall{2,#}(x12,x13) ->
     forall{2,#}(p,cons2(x,xs)) -> forall{2,#}(p,xs)
     forall{2,#}(p,cons2(x,xs)) -> app#(p,x) ->
     app#(forsome1(x19),x20) -> forsome{2,#}(x19,x20)
     forall{2,#}(p,cons2(x,xs)) -> app#(p,x) ->
     app#(forall1(x12),x13) -> forall{2,#}(x12,x13)
     forall{2,#}(p,cons2(x,xs)) -> app#(p,x) ->
     app#(or1(x9),x10) -> or{2,#}(x9,x10)
     forall{2,#}(p,cons2(x,xs)) -> app#(p,x) ->
     app#(and1(x4),x5) -> and{2,#}(x4,x5)
     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(x12),x13) -> forall{2,#}(x12,x13)
      forall{2,#}(p,cons2(x,xs)) -> forall{2,#}(p,xs)
      forall{2,#}(p,cons2(x,xs)) -> app#(p,x)
      app#(forsome1(x19),x20) -> forsome{2,#}(x19,x20)
     TRS:
      and2(true0(),true0()) -> true0()
      and2(x,false0()) -> false0()
      and2(false0(),y) -> false0()
      or2(true0(),y) -> true0()
      or2(x,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(x4),x5) -> and2(x4,x5)
      app(and0(),x4) -> and1(x4)
      app(or1(x9),x10) -> or2(x9,x10)
      app(or0(),x9) -> or1(x9)
      app(forall1(x12),x13) -> forall2(x12,x13)
      app(forall0(),x12) -> forall1(x12)
      app(cons1(x16),x17) -> cons2(x16,x17)
      app(cons0(),x16) -> cons1(x16)
      app(forsome1(x19),x20) -> forsome2(x19,x20)
      app(forsome0(),x19) -> forsome1(x19)
     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(x,false0()) -> false0()
        and2(false0(),y) -> false0()
        or2(true0(),y) -> true0()
        or2(x,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(x4),x5) -> and2(x4,x5)
        app(and0(),x4) -> and1(x4)
        app(or1(x9),x10) -> or2(x9,x10)
        app(or0(),x9) -> or1(x9)
        app(forall1(x12),x13) -> forall2(x12,x13)
        app(forall0(),x12) -> forall1(x12)
        app(cons1(x16),x17) -> cons2(x16,x17)
        app(cons0(),x16) -> cons1(x16)
        app(forsome1(x19),x20) -> forsome2(x19,x20)
        app(forsome0(),x19) -> forsome1(x19)
      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(x,false0()) -> false0()
        and2(false0(),y) -> false0()
        or2(true0(),y) -> true0()
        or2(x,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(x4),x5) -> and2(x4,x5)
        app(and0(),x4) -> and1(x4)
        app(or1(x9),x10) -> or2(x9,x10)
        app(or0(),x9) -> or1(x9)
        app(forall1(x12),x13) -> forall2(x12,x13)
        app(forall0(),x12) -> forall1(x12)
        app(cons1(x16),x17) -> cons2(x16,x17)
        app(cons0(),x16) -> cons1(x16)
        app(forsome1(x19),x20) -> forsome2(x19,x20)
        app(forsome0(),x19) -> forsome1(x19)
       Subterm Criterion Processor:
        simple projection:
         pi(forall{2,#}) = 1
        problem:
         DPs:
          
         TRS:
          and2(true0(),true0()) -> true0()
          and2(x,false0()) -> false0()
          and2(false0(),y) -> false0()
          or2(true0(),y) -> true0()
          or2(x,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(x4),x5) -> and2(x4,x5)
          app(and0(),x4) -> and1(x4)
          app(or1(x9),x10) -> or2(x9,x10)
          app(or0(),x9) -> or1(x9)
          app(forall1(x12),x13) -> forall2(x12,x13)
          app(forall0(),x12) -> forall1(x12)
          app(cons1(x16),x17) -> cons2(x16,x17)
          app(cons0(),x16) -> cons1(x16)
          app(forsome1(x19),x20) -> forsome2(x19,x20)
          app(forsome0(),x19) -> forsome1(x19)
        Qed
       
       DPs:
        forsome{2,#}(p,cons2(x,xs)) -> forsome{2,#}(p,xs)
       TRS:
        and2(true0(),true0()) -> true0()
        and2(x,false0()) -> false0()
        and2(false0(),y) -> false0()
        or2(true0(),y) -> true0()
        or2(x,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(x4),x5) -> and2(x4,x5)
        app(and0(),x4) -> and1(x4)
        app(or1(x9),x10) -> or2(x9,x10)
        app(or0(),x9) -> or1(x9)
        app(forall1(x12),x13) -> forall2(x12,x13)
        app(forall0(),x12) -> forall1(x12)
        app(cons1(x16),x17) -> cons2(x16,x17)
        app(cons0(),x16) -> cons1(x16)
        app(forsome1(x19),x20) -> forsome2(x19,x20)
        app(forsome0(),x19) -> forsome1(x19)
       Subterm Criterion Processor:
        simple projection:
         pi(forsome{2,#}) = 1
        problem:
         DPs:
          
         TRS:
          and2(true0(),true0()) -> true0()
          and2(x,false0()) -> false0()
          and2(false0(),y) -> false0()
          or2(true0(),y) -> true0()
          or2(x,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(x4),x5) -> and2(x4,x5)
          app(and0(),x4) -> and1(x4)
          app(or1(x9),x10) -> or2(x9,x10)
          app(or0(),x9) -> or1(x9)
          app(forall1(x12),x13) -> forall2(x12,x13)
          app(forall0(),x12) -> forall1(x12)
          app(cons1(x16),x17) -> cons2(x16,x17)
          app(cons0(),x16) -> cons1(x16)
          app(forsome1(x19),x20) -> forsome2(x19,x20)
          app(forsome0(),x19) -> forsome1(x19)
        Qed