/export/starexec/sandbox2/solver/bin/starexec_run_tct_rci /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/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:
            foldr#3(Cons(x16,x6)) -> step_x_f(rev_l(),x16,foldr#3(x6))
            foldr#3(Nil()) -> fleft_op_e_xs_1()
            main(Cons(x8,x9)) -> step_x_f#1(rev_l(),x8,foldr#3(x9),Nil())
            main(Nil()) -> Nil()
            rev_l#2(x8,x10) -> Cons(x10,x8)
            step_x_f#1(rev_l(),x5,fleft_op_e_xs_1(),x3) -> rev_l#2(x3,x5)
            step_x_f#1(rev_l(),x5,step_x_f(x2,x3,x4),x1) -> step_x_f#1(x2,x3,x4,rev_l#2(x1,x5))
        - Signature:
            {foldr#3/1,main/1,rev_l#2/2,step_x_f#1/4} / {Cons/2,Nil/0,fleft_op_e_xs_1/0,rev_l/0,step_x_f/3}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {foldr#3,main,rev_l#2,step_x_f#1} and constructors {Cons
            ,Nil,fleft_op_e_xs_1,rev_l,step_x_f}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            foldr#3(Cons(x16,x6)) -> step_x_f(rev_l(),x16,foldr#3(x6))
            foldr#3(Nil()) -> fleft_op_e_xs_1()
            main(Cons(x8,x9)) -> step_x_f#1(rev_l(),x8,foldr#3(x9),Nil())
            main(Nil()) -> Nil()
            rev_l#2(x8,x10) -> Cons(x10,x8)
            step_x_f#1(rev_l(),x5,fleft_op_e_xs_1(),x3) -> rev_l#2(x3,x5)
            step_x_f#1(rev_l(),x5,step_x_f(x2,x3,x4),x1) -> step_x_f#1(x2,x3,x4,rev_l#2(x1,x5))
        - Signature:
            {foldr#3/1,main/1,rev_l#2/2,step_x_f#1/4} / {Cons/2,Nil/0,fleft_op_e_xs_1/0,rev_l/0,step_x_f/3}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {foldr#3,main,rev_l#2,step_x_f#1} and constructors {Cons
            ,Nil,fleft_op_e_xs_1,rev_l,step_x_f}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          foldr#3(y){y -> Cons(x,y)} =
            foldr#3(Cons(x,y)) ->^+ step_x_f(rev_l(),x,foldr#3(y))
              = C[foldr#3(y) = foldr#3(y){}]

** Step 1.b:1: Ara WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            foldr#3(Cons(x16,x6)) -> step_x_f(rev_l(),x16,foldr#3(x6))
            foldr#3(Nil()) -> fleft_op_e_xs_1()
            main(Cons(x8,x9)) -> step_x_f#1(rev_l(),x8,foldr#3(x9),Nil())
            main(Nil()) -> Nil()
            rev_l#2(x8,x10) -> Cons(x10,x8)
            step_x_f#1(rev_l(),x5,fleft_op_e_xs_1(),x3) -> rev_l#2(x3,x5)
            step_x_f#1(rev_l(),x5,step_x_f(x2,x3,x4),x1) -> step_x_f#1(x2,x3,x4,rev_l#2(x1,x5))
        - Signature:
            {foldr#3/1,main/1,rev_l#2/2,step_x_f#1/4} / {Cons/2,Nil/0,fleft_op_e_xs_1/0,rev_l/0,step_x_f/3}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {foldr#3,main,rev_l#2,step_x_f#1} and constructors {Cons
            ,Nil,fleft_op_e_xs_1,rev_l,step_x_f}
    + Applied Processor:
        Ara {araHeuristics = NoHeuristics, minDegree = 1, maxDegree = 2, araTimeout = 5, araRuleShifting = Nothing}
    + Details:
        Signatures used:
        ----------------
          Cons :: ["A"(14) x "A"(14)] -(14)-> "A"(14)
          Cons :: ["A"(15) x "A"(15)] -(15)-> "A"(15)
          Cons :: ["A"(0) x "A"(0)] -(0)-> "A"(0)
          Nil :: [] -(0)-> "A"(14)
          Nil :: [] -(0)-> "A"(15)
          Nil :: [] -(0)-> "A"(2)
          Nil :: [] -(0)-> "A"(0)
          fleft_op_e_xs_1 :: [] -(0)-> "A"(8)
          fleft_op_e_xs_1 :: [] -(0)-> "A"(12)
          foldr#3 :: ["A"(14)] -(10)-> "A"(8)
          main :: ["A"(15)] -(11)-> "A"(0)
          rev_l :: [] -(0)-> "A"(4)
          rev_l :: [] -(0)-> "A"(8)
          rev_l#2 :: ["A"(0) x "A"(0)] -(1)-> "A"(0)
          step_x_f :: ["A"(8) x "A"(0) x "A"(8)] -(8)-> "A"(8)
          step_x_f#1 :: ["A"(4) x "A"(0) x "A"(8) x "A"(0)] -(12)-> "A"(0)
        
        
        Cost-free Signatures used:
        --------------------------
        
        
        
        Base Constructor Signatures used:
        ---------------------------------
          "Cons_A" :: ["A"(1) x "A"(1)] -(1)-> "A"(1)
          "Nil_A" :: [] -(0)-> "A"(1)
          "fleft_op_e_xs_1_A" :: [] -(0)-> "A"(1)
          "rev_l_A" :: [] -(0)-> "A"(1)
          "step_x_f_A" :: ["A"(0) x "A"(0) x "A"(0)] -(1)-> "A"(1)
        

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