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


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WORST_CASE(Omega(n^1),O(n^1))
* Step 1: Sum WORST_CASE(Omega(n^1),O(n^1))
    + Considered Problem:
        - Strict TRS:
            fold(a,xs) -> Cons(foldl(a,xs),Cons(foldr(a,xs),Nil()))
            foldl(a,Nil()) -> a
            foldl(x,Cons(S(0()),xs)) -> foldl(S(x),xs)
            foldl(S(0()),Cons(x,xs)) -> foldl(S(x),xs)
            foldr(a,Cons(x,xs)) -> op(x,foldr(a,xs))
            foldr(a,Nil()) -> a
            notEmpty(Cons(x,xs)) -> True()
            notEmpty(Nil()) -> False()
            op(x,S(0())) -> S(x)
            op(S(0()),y) -> S(y)
        - Signature:
            {fold/2,foldl/2,foldr/2,notEmpty/1,op/2} / {0/0,Cons/2,False/0,Nil/0,S/1,True/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {fold,foldl,foldr,notEmpty,op} and constructors {0,Cons
            ,False,Nil,S,True}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            fold(a,xs) -> Cons(foldl(a,xs),Cons(foldr(a,xs),Nil()))
            foldl(a,Nil()) -> a
            foldl(x,Cons(S(0()),xs)) -> foldl(S(x),xs)
            foldl(S(0()),Cons(x,xs)) -> foldl(S(x),xs)
            foldr(a,Cons(x,xs)) -> op(x,foldr(a,xs))
            foldr(a,Nil()) -> a
            notEmpty(Cons(x,xs)) -> True()
            notEmpty(Nil()) -> False()
            op(x,S(0())) -> S(x)
            op(S(0()),y) -> S(y)
        - Signature:
            {fold/2,foldl/2,foldr/2,notEmpty/1,op/2} / {0/0,Cons/2,False/0,Nil/0,S/1,True/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {fold,foldl,foldr,notEmpty,op} and constructors {0,Cons
            ,False,Nil,S,True}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          foldl(x,y){y -> Cons(S(0()),y)} =
            foldl(x,Cons(S(0()),y)) ->^+ foldl(S(x),y)
              = C[foldl(S(x),y) = foldl(x,y){x -> S(x)}]

** Step 1.b:1: Ara WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            fold(a,xs) -> Cons(foldl(a,xs),Cons(foldr(a,xs),Nil()))
            foldl(a,Nil()) -> a
            foldl(x,Cons(S(0()),xs)) -> foldl(S(x),xs)
            foldl(S(0()),Cons(x,xs)) -> foldl(S(x),xs)
            foldr(a,Cons(x,xs)) -> op(x,foldr(a,xs))
            foldr(a,Nil()) -> a
            notEmpty(Cons(x,xs)) -> True()
            notEmpty(Nil()) -> False()
            op(x,S(0())) -> S(x)
            op(S(0()),y) -> S(y)
        - Signature:
            {fold/2,foldl/2,foldr/2,notEmpty/1,op/2} / {0/0,Cons/2,False/0,Nil/0,S/1,True/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {fold,foldl,foldr,notEmpty,op} and constructors {0,Cons
            ,False,Nil,S,True}
    + Applied Processor:
        Ara {araHeuristics = NoHeuristics, minDegree = 1, maxDegree = 2, araTimeout = 5, araRuleShifting = Nothing}
    + Details:
        Signatures used:
        ----------------
          0 :: [] -(0)-> "A"(0)
          Cons :: ["A"(0) x "A"(13)] -(13)-> "A"(13)
          Cons :: ["A"(0) x "A"(2)] -(2)-> "A"(2)
          Cons :: ["A"(0) x "A"(7)] -(7)-> "A"(7)
          Cons :: ["A"(0) x "A"(0)] -(0)-> "A"(0)
          False :: [] -(0)-> "A"(0)
          Nil :: [] -(0)-> "A"(13)
          Nil :: [] -(0)-> "A"(2)
          Nil :: [] -(0)-> "A"(7)
          Nil :: [] -(0)-> "A"(12)
          S :: ["A"(0)] -(0)-> "A"(0)
          S :: ["A"(0)] -(11)-> "A"(11)
          S :: ["A"(0)] -(15)-> "A"(15)
          True :: [] -(0)-> "A"(0)
          fold :: ["A"(13) x "A"(15)] -(16)-> "A"(0)
          foldl :: ["A"(11) x "A"(13)] -(8)-> "A"(2)
          foldr :: ["A"(1) x "A"(2)] -(1)-> "A"(0)
          notEmpty :: ["A"(7)] -(1)-> "A"(0)
          op :: ["A"(0) x "A"(0)] -(1)-> "A"(0)
        
        
        Cost-free Signatures used:
        --------------------------
        
        
        
        Base Constructor Signatures used:
        ---------------------------------
          "0_A" :: [] -(0)-> "A"(1)
          "Cons_A" :: ["A"(0) x "A"(1)] -(1)-> "A"(1)
          "False_A" :: [] -(0)-> "A"(1)
          "Nil_A" :: [] -(0)-> "A"(1)
          "S_A" :: ["A"(0)] -(1)-> "A"(1)
          "True_A" :: [] -(0)-> "A"(1)
        

WORST_CASE(Omega(n^1),O(n^1))