/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:
            comp_f_g#1(comp_f_g(x4,x5),comp_f_g(x2,x3),x1) -> comp_f_g#1(x4,x5,comp_f_g#1(x2,x3,x1))
            comp_f_g#1(comp_f_g(x7,x9),cons_x(x2),x4) -> comp_f_g#1(x7,x9,Cons(x2,x4))
            comp_f_g#1(cons_x(x2),comp_f_g(x5,x7),x3) -> Cons(x2,comp_f_g#1(x5,x7,x3))
            comp_f_g#1(cons_x(x5),cons_x(x2),x4) -> Cons(x5,Cons(x2,x4))
            main(Leaf(x4)) -> Cons(x4,Nil())
            main(Node(x9,x5)) -> comp_f_g#1(walk#1(x9),walk#1(x5),Nil())
            walk#1(Leaf(x2)) -> cons_x(x2)
            walk#1(Node(x5,x3)) -> comp_f_g(walk#1(x5),walk#1(x3))
        - Signature:
            {comp_f_g#1/3,main/1,walk#1/1} / {Cons/2,Leaf/1,Nil/0,Node/2,comp_f_g/2,cons_x/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {comp_f_g#1,main,walk#1} and constructors {Cons,Leaf,Nil
            ,Node,comp_f_g,cons_x}
    + 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(x4,x5),comp_f_g(x2,x3),x1) -> comp_f_g#1(x4,x5,comp_f_g#1(x2,x3,x1))
            comp_f_g#1(comp_f_g(x7,x9),cons_x(x2),x4) -> comp_f_g#1(x7,x9,Cons(x2,x4))
            comp_f_g#1(cons_x(x2),comp_f_g(x5,x7),x3) -> Cons(x2,comp_f_g#1(x5,x7,x3))
            comp_f_g#1(cons_x(x5),cons_x(x2),x4) -> Cons(x5,Cons(x2,x4))
            main(Leaf(x4)) -> Cons(x4,Nil())
            main(Node(x9,x5)) -> comp_f_g#1(walk#1(x9),walk#1(x5),Nil())
            walk#1(Leaf(x2)) -> cons_x(x2)
            walk#1(Node(x5,x3)) -> comp_f_g(walk#1(x5),walk#1(x3))
        - Signature:
            {comp_f_g#1/3,main/1,walk#1/1} / {Cons/2,Leaf/1,Nil/0,Node/2,comp_f_g/2,cons_x/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {comp_f_g#1,main,walk#1} and constructors {Cons,Leaf,Nil
            ,Node,comp_f_g,cons_x}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          walk#1(x){x -> Node(x,y)} =
            walk#1(Node(x,y)) ->^+ comp_f_g(walk#1(x),walk#1(y))
              = C[walk#1(x) = walk#1(x){}]

** Step 1.b:1: Ara WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            comp_f_g#1(comp_f_g(x4,x5),comp_f_g(x2,x3),x1) -> comp_f_g#1(x4,x5,comp_f_g#1(x2,x3,x1))
            comp_f_g#1(comp_f_g(x7,x9),cons_x(x2),x4) -> comp_f_g#1(x7,x9,Cons(x2,x4))
            comp_f_g#1(cons_x(x2),comp_f_g(x5,x7),x3) -> Cons(x2,comp_f_g#1(x5,x7,x3))
            comp_f_g#1(cons_x(x5),cons_x(x2),x4) -> Cons(x5,Cons(x2,x4))
            main(Leaf(x4)) -> Cons(x4,Nil())
            main(Node(x9,x5)) -> comp_f_g#1(walk#1(x9),walk#1(x5),Nil())
            walk#1(Leaf(x2)) -> cons_x(x2)
            walk#1(Node(x5,x3)) -> comp_f_g(walk#1(x5),walk#1(x3))
        - Signature:
            {comp_f_g#1/3,main/1,walk#1/1} / {Cons/2,Leaf/1,Nil/0,Node/2,comp_f_g/2,cons_x/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {comp_f_g#1,main,walk#1} and constructors {Cons,Leaf,Nil
            ,Node,comp_f_g,cons_x}
    + Applied Processor:
        Ara {araHeuristics = NoHeuristics, minDegree = 1, maxDegree = 2, araTimeout = 5, araRuleShifting = Nothing}
    + Details:
        Signatures used:
        ----------------
          Cons :: ["A"(4) x "A"(0)] -(4)-> "A"(4)
          Cons :: ["A"(12) x "A"(0)] -(12)-> "A"(12)
          Cons :: ["A"(9) x "A"(0)] -(9)-> "A"(9)
          Cons :: ["A"(2) x "A"(0)] -(2)-> "A"(2)
          Cons :: ["A"(7) x "A"(0)] -(7)-> "A"(7)
          Leaf :: ["A"(15)] -(15)-> "A"(15)
          Nil :: [] -(0)-> "A"(12)
          Nil :: [] -(0)-> "A"(9)
          Node :: ["A"(15) x "A"(15)] -(15)-> "A"(15)
          comp_f_g :: ["A"(12) x "A"(12)] -(12)-> "A"(12)
          comp_f_g#1 :: ["A"(12) x "A"(12) x "A"(3)] -(0)-> "A"(8)
          cons_x :: ["A"(12)] -(12)-> "A"(12)
          cons_x :: ["A"(15)] -(15)-> "A"(15)
          main :: ["A"(15)] -(11)-> "A"(2)
          walk#1 :: ["A"(15)] -(1)-> "A"(12)
        
        
        Cost-free Signatures used:
        --------------------------
        
        
        
        Base Constructor Signatures used:
        ---------------------------------
          "Cons_A" :: ["A"(1) x "A"(0)] -(1)-> "A"(1)
          "Leaf_A" :: ["A"(1)] -(1)-> "A"(1)
          "Nil_A" :: [] -(0)-> "A"(1)
          "Node_A" :: ["A"(1) x "A"(1)] -(1)-> "A"(1)
          "comp_f_g_A" :: ["A"(0) x "A"(0)] -(1)-> "A"(1)
          "cons_x_A" :: ["A"(0)] -(1)-> "A"(1)
        

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