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


--------------------------------------------------------------------------------


WORST_CASE(?,O(n^1))
* Step 1: Sum WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            dec(Cons(Cons(x,xs),Nil())) -> dec(Nil())
            dec(Cons(Cons(x',xs'),Cons(x,xs))) -> dec(Cons(x,xs))
            dec(Cons(Nil(),Cons(x,xs))) -> dec(Cons(x,xs))
            dec(Cons(Nil(),Nil())) -> Nil()
            goal(x) -> nestdec(x)
            isNilNil(Cons(Cons(x,xs),Nil())) -> False()
            isNilNil(Cons(Cons(x',xs'),Cons(x,xs))) -> False()
            isNilNil(Cons(Nil(),Cons(x,xs))) -> False()
            isNilNil(Cons(Nil(),Nil())) -> True()
            nestdec(Cons(x,xs)) -> nestdec(dec(Cons(x,xs)))
            nestdec(Nil()) -> Cons(Nil()
                                  ,Cons(Nil()
                                       ,Cons(Nil()
                                            ,Cons(Nil()
                                                 ,Cons(Nil()
                                                      ,Cons(Nil()
                                                           ,Cons(Nil()
                                                                ,Cons(Nil()
                                                                     ,Cons(Nil()
                                                                          ,Cons(Nil()
                                                                               ,Cons(Nil()
                                                                                    ,Cons(Nil()
                                                                                         ,Cons(Nil()
                                                                                              ,Cons(Nil()
                                                                                                   ,Cons(Nil()
                                                                                                        ,Cons(Nil()
                                                                                                             ,Cons(Nil()
                                                                                                                  ,Nil())))))))))))))))))
            number17(n) -> Cons(Nil()
                               ,Cons(Nil()
                                    ,Cons(Nil()
                                         ,Cons(Nil()
                                              ,Cons(Nil()
                                                   ,Cons(Nil()
                                                        ,Cons(Nil()
                                                             ,Cons(Nil()
                                                                  ,Cons(Nil()
                                                                       ,Cons(Nil()
                                                                            ,Cons(Nil()
                                                                                 ,Cons(Nil()
                                                                                      ,Cons(Nil()
                                                                                           ,Cons(Nil()
                                                                                                ,Cons(Nil()
                                                                                                     ,Cons(Nil()
                                                                                                          ,Cons(Nil()
                                                                                                               ,Nil())))))))))))))))))
        - Signature:
            {dec/1,goal/1,isNilNil/1,nestdec/1,number17/1} / {Cons/2,False/0,Nil/0,True/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {dec,goal,isNilNil,nestdec
            ,number17} and constructors {Cons,False,Nil,True}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Ara WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            dec(Cons(Cons(x,xs),Nil())) -> dec(Nil())
            dec(Cons(Cons(x',xs'),Cons(x,xs))) -> dec(Cons(x,xs))
            dec(Cons(Nil(),Cons(x,xs))) -> dec(Cons(x,xs))
            dec(Cons(Nil(),Nil())) -> Nil()
            goal(x) -> nestdec(x)
            isNilNil(Cons(Cons(x,xs),Nil())) -> False()
            isNilNil(Cons(Cons(x',xs'),Cons(x,xs))) -> False()
            isNilNil(Cons(Nil(),Cons(x,xs))) -> False()
            isNilNil(Cons(Nil(),Nil())) -> True()
            nestdec(Cons(x,xs)) -> nestdec(dec(Cons(x,xs)))
            nestdec(Nil()) -> Cons(Nil()
                                  ,Cons(Nil()
                                       ,Cons(Nil()
                                            ,Cons(Nil()
                                                 ,Cons(Nil()
                                                      ,Cons(Nil()
                                                           ,Cons(Nil()
                                                                ,Cons(Nil()
                                                                     ,Cons(Nil()
                                                                          ,Cons(Nil()
                                                                               ,Cons(Nil()
                                                                                    ,Cons(Nil()
                                                                                         ,Cons(Nil()
                                                                                              ,Cons(Nil()
                                                                                                   ,Cons(Nil()
                                                                                                        ,Cons(Nil()
                                                                                                             ,Cons(Nil()
                                                                                                                  ,Nil())))))))))))))))))
            number17(n) -> Cons(Nil()
                               ,Cons(Nil()
                                    ,Cons(Nil()
                                         ,Cons(Nil()
                                              ,Cons(Nil()
                                                   ,Cons(Nil()
                                                        ,Cons(Nil()
                                                             ,Cons(Nil()
                                                                  ,Cons(Nil()
                                                                       ,Cons(Nil()
                                                                            ,Cons(Nil()
                                                                                 ,Cons(Nil()
                                                                                      ,Cons(Nil()
                                                                                           ,Cons(Nil()
                                                                                                ,Cons(Nil()
                                                                                                     ,Cons(Nil()
                                                                                                          ,Cons(Nil()
                                                                                                               ,Nil())))))))))))))))))
        - Signature:
            {dec/1,goal/1,isNilNil/1,nestdec/1,number17/1} / {Cons/2,False/0,Nil/0,True/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {dec,goal,isNilNil,nestdec
            ,number17} and constructors {Cons,False,Nil,True}
    + Applied Processor:
        Ara {araHeuristics = NoHeuristics, minDegree = 1, maxDegree = 2, araTimeout = 5, araRuleShifting = Nothing}
    + Details:
        Signatures used:
        ----------------
          Cons :: ["A"(5) x "A"(5)] -(5)-> "A"(5)
          Cons :: ["A"(15) x "A"(15)] -(15)-> "A"(15)
          Cons :: ["A"(0) x "A"(0)] -(0)-> "A"(0)
          Cons :: ["A"(1) x "A"(1)] -(1)-> "A"(1)
          False :: [] -(0)-> "A"(0)
          Nil :: [] -(0)-> "A"(5)
          Nil :: [] -(0)-> "A"(15)
          Nil :: [] -(0)-> "A"(8)
          Nil :: [] -(0)-> "A"(12)
          Nil :: [] -(0)-> "A"(9)
          Nil :: [] -(0)-> "A"(13)
          True :: [] -(0)-> "A"(0)
          dec :: ["A"(5)] -(9)-> "A"(15)
          goal :: ["A"(15)] -(16)-> "A"(0)
          isNilNil :: ["A"(5)] -(0)-> "A"(0)
          nestdec :: ["A"(15)] -(4)-> "A"(0)
          number17 :: ["A"(0)] -(16)-> "A"(0)
        
        
        Cost-free Signatures used:
        --------------------------
        
        
        
        Base Constructor Signatures used:
        ---------------------------------
          "Cons_A" :: ["A"(1) x "A"(1)] -(1)-> "A"(1)
          "False_A" :: [] -(0)-> "A"(1)
          "Nil_A" :: [] -(0)-> "A"(1)
          "True_A" :: [] -(0)-> "A"(1)
        

WORST_CASE(?,O(n^1))