/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:
            comp_f_g#1(comp_f_g(x7,x9),walk_xs_3(x8),x12) -> comp_f_g#1(x7,x9,Cons(x8,x12))
            comp_f_g#1(walk_xs(),walk_xs_3(x8),x12) -> Cons(x8,x12)
            main(Cons(x4,x5)) -> comp_f_g#1(walk#1(x5),walk_xs_3(x4),Nil())
            main(Nil()) -> Nil()
            walk#1(Cons(x4,x3)) -> comp_f_g(walk#1(x3),walk_xs_3(x4))
            walk#1(Nil()) -> walk_xs()
        - Signature:
            {comp_f_g#1/3,main/1,walk#1/1} / {Cons/2,Nil/0,comp_f_g/2,walk_xs/0,walk_xs_3/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {comp_f_g#1,main,walk#1} and constructors {Cons,Nil
            ,comp_f_g,walk_xs,walk_xs_3}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            comp_f_g#1(comp_f_g(x7,x9),walk_xs_3(x8),x12) -> comp_f_g#1(x7,x9,Cons(x8,x12))
            comp_f_g#1(walk_xs(),walk_xs_3(x8),x12) -> Cons(x8,x12)
            main(Cons(x4,x5)) -> comp_f_g#1(walk#1(x5),walk_xs_3(x4),Nil())
            main(Nil()) -> Nil()
            walk#1(Cons(x4,x3)) -> comp_f_g(walk#1(x3),walk_xs_3(x4))
            walk#1(Nil()) -> walk_xs()
        - Signature:
            {comp_f_g#1/3,main/1,walk#1/1} / {Cons/2,Nil/0,comp_f_g/2,walk_xs/0,walk_xs_3/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {comp_f_g#1,main,walk#1} and constructors {Cons,Nil
            ,comp_f_g,walk_xs,walk_xs_3}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          walk#1(y){y -> Cons(x,y)} =
            walk#1(Cons(x,y)) ->^+ comp_f_g(walk#1(y),walk_xs_3(x))
              = C[walk#1(y) = walk#1(y){}]

** Step 1.b:1: Ara WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            comp_f_g#1(comp_f_g(x7,x9),walk_xs_3(x8),x12) -> comp_f_g#1(x7,x9,Cons(x8,x12))
            comp_f_g#1(walk_xs(),walk_xs_3(x8),x12) -> Cons(x8,x12)
            main(Cons(x4,x5)) -> comp_f_g#1(walk#1(x5),walk_xs_3(x4),Nil())
            main(Nil()) -> Nil()
            walk#1(Cons(x4,x3)) -> comp_f_g(walk#1(x3),walk_xs_3(x4))
            walk#1(Nil()) -> walk_xs()
        - Signature:
            {comp_f_g#1/3,main/1,walk#1/1} / {Cons/2,Nil/0,comp_f_g/2,walk_xs/0,walk_xs_3/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {comp_f_g#1,main,walk#1} and constructors {Cons,Nil
            ,comp_f_g,walk_xs,walk_xs_3}
    + Applied Processor:
        Ara {araHeuristics = NoHeuristics, minDegree = 1, maxDegree = 2, araTimeout = 5, araRuleShifting = Nothing}
    + Details:
        Signatures used:
        ----------------
          Cons :: ["A"(15) x "A"(15)] -(15)-> "A"(15)
          Cons :: ["A"(13) x "A"(13)] -(13)-> "A"(13)
          Cons :: ["A"(0) x "A"(0)] -(0)-> "A"(0)
          Nil :: [] -(0)-> "A"(15)
          Nil :: [] -(0)-> "A"(13)
          Nil :: [] -(0)-> "A"(12)
          Nil :: [] -(0)-> "A"(0)
          comp_f_g :: ["A"(8) x "A"(8)] -(8)-> "A"(8)
          comp_f_g#1 :: ["A"(8) x "A"(0) x "A"(0)] -(1)-> "A"(0)
          main :: ["A"(15)] -(12)-> "A"(0)
          walk#1 :: ["A"(13)] -(1)-> "A"(8)
          walk_xs :: [] -(0)-> "A"(8)
          walk_xs :: [] -(0)-> "A"(9)
          walk_xs_3 :: ["A"(0)] -(0)-> "A"(0)
          walk_xs_3 :: ["A"(14)] -(0)-> "A"(14)
          walk_xs_3 :: ["A"(13)] -(0)-> "A"(13)
        
        
        Cost-free Signatures used:
        --------------------------
        
        
        
        Base Constructor Signatures used:
        ---------------------------------
          "Cons_A" :: ["A"(1) x "A"(1)] -(1)-> "A"(1)
          "Nil_A" :: [] -(0)-> "A"(1)
          "comp_f_g_A" :: ["A"(0) x "A"(0)] -(1)-> "A"(1)
          "walk_xs_3_A" :: ["A"(0)] -(0)-> "A"(1)
          "walk_xs_A" :: [] -(0)-> "A"(1)
        

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