Runti Compl Inner Rewri 22807 pair #381904027

details

property	value
status	complete
benchmark	flatten.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n055.star.cs.uiowa.edu
space	hoca

run statistics

property	value
solver	tct 2018-07-13
configuration	tct_rci
runtime (wallclock)	0.472978115082 seconds
cpu usage	1.912758093
max memory	4.3311104E7

stage attributes

key	value
output-size	5023
starexec-result	WORST_CASE(Omega(n^1),O(n^1))

output

/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)

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