Runti Compl Inner Rewri 22807 pair #381904200

details

property	value
status	complete
benchmark	thetrickSize.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n042.star.cs.uiowa.edu
space	Frederiksen_Others

run statistics

property	value
solver	tct 2018-07-13
configuration	tct_rci
runtime (wallclock)	3.72303795815 seconds
cpu usage	14.776717153
max memory	1.25087744E8

stage attributes

key	value
output-size	7289
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:
            f(x,Cons(x',xs)) -> f[Ite][False][Ite](lt0(x,Cons(Nil(),Nil())),x,Cons(x',xs))
            f(x,Nil()) -> Cons(Nil(),Cons(Nil(),Cons(Nil(),Cons(Nil(),Nil()))))
            g(x,Cons(x',xs)) -> g[Ite][False][Ite](lt0(x,Cons(Nil(),Nil())),x,Cons(x',xs))
            g(x,Nil()) -> Cons(Nil(),Cons(Nil(),Cons(Nil(),Cons(Nil(),Nil()))))
            goal(x,y) -> Cons(f(x,y),Cons(g(x,y),Nil()))
            lt0(x,Nil()) -> False()
            lt0(Cons(x',xs'),Cons(x,xs)) -> lt0(xs',xs)
            lt0(Nil(),Cons(x',xs)) -> True()
            notEmpty(Cons(x,xs)) -> True()
            notEmpty(Nil()) -> False()
            number4(n) -> Cons(Nil(),Cons(Nil(),Cons(Nil(),Cons(Nil(),Nil()))))
        - Weak TRS:
            f[Ite][False][Ite](False(),Cons(x,xs),y) -> f(xs,Cons(Cons(Nil(),Nil()),y))
            f[Ite][False][Ite](True(),x',Cons(x,xs)) -> f(x',xs)
            g[Ite][False][Ite](False(),Cons(x,xs),y) -> g(xs,Cons(Cons(Nil(),Nil()),y))
            g[Ite][False][Ite](True(),x',Cons(x,xs)) -> g(x',xs)
        - Signature:
            {f/2,f[Ite][False][Ite]/3,g/2,g[Ite][False][Ite]/3,goal/2,lt0/2,notEmpty/1,number4/1} / {Cons/2,False/0
            ,Nil/0,True/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,f[Ite][False][Ite],g,g[Ite][False][Ite],goal,lt0
            ,notEmpty,number4} and constructors {Cons,False,Nil,True}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            f(x,Cons(x',xs)) -> f[Ite][False][Ite](lt0(x,Cons(Nil(),Nil())),x,Cons(x',xs))
            f(x,Nil()) -> Cons(Nil(),Cons(Nil(),Cons(Nil(),Cons(Nil(),Nil()))))
            g(x,Cons(x',xs)) -> g[Ite][False][Ite](lt0(x,Cons(Nil(),Nil())),x,Cons(x',xs))
            g(x,Nil()) -> Cons(Nil(),Cons(Nil(),Cons(Nil(),Cons(Nil(),Nil()))))
            goal(x,y) -> Cons(f(x,y),Cons(g(x,y),Nil()))
            lt0(x,Nil()) -> False()
            lt0(Cons(x',xs'),Cons(x,xs)) -> lt0(xs',xs)
            lt0(Nil(),Cons(x',xs)) -> True()
            notEmpty(Cons(x,xs)) -> True()
            notEmpty(Nil()) -> False()
            number4(n) -> Cons(Nil(),Cons(Nil(),Cons(Nil(),Cons(Nil(),Nil()))))
        - Weak TRS:
            f[Ite][False][Ite](False(),Cons(x,xs),y) -> f(xs,Cons(Cons(Nil(),Nil()),y))
            f[Ite][False][Ite](True(),x',Cons(x,xs)) -> f(x',xs)
            g[Ite][False][Ite](False(),Cons(x,xs),y) -> g(xs,Cons(Cons(Nil(),Nil()),y))
            g[Ite][False][Ite](True(),x',Cons(x,xs)) -> g(x',xs)
        - Signature:
            {f/2,f[Ite][False][Ite]/3,g/2,g[Ite][False][Ite]/3,goal/2,lt0/2,notEmpty/1,number4/1} / {Cons/2,False/0
            ,Nil/0,True/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,f[Ite][False][Ite],g,g[Ite][False][Ite],goal,lt0
            ,notEmpty,number4} and constructors {Cons,False,Nil,True}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          lt0(y,u){y -> Cons(x,y),u -> Cons(z,u)} =
            lt0(Cons(x,y),Cons(z,u)) ->^+ lt0(y,u)
              = C[lt0(y,u) = lt0(y,u){}]

** Step 1.b:1: Ara WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            f(x,Cons(x',xs)) -> f[Ite][False][Ite](lt0(x,Cons(Nil(),Nil())),x,Cons(x',xs))
            f(x,Nil()) -> Cons(Nil(),Cons(Nil(),Cons(Nil(),Cons(Nil(),Nil()))))
            g(x,Cons(x',xs)) -> g[Ite][False][Ite](lt0(x,Cons(Nil(),Nil())),x,Cons(x',xs))
            g(x,Nil()) -> Cons(Nil(),Cons(Nil(),Cons(Nil(),Cons(Nil(),Nil()))))
            goal(x,y) -> Cons(f(x,y),Cons(g(x,y),Nil()))
            lt0(x,Nil()) -> False()
            lt0(Cons(x',xs'),Cons(x,xs)) -> lt0(xs',xs)
            lt0(Nil(),Cons(x',xs)) -> True()
            notEmpty(Cons(x,xs)) -> True()
            notEmpty(Nil()) -> False()
            number4(n) -> Cons(Nil(),Cons(Nil(),Cons(Nil(),Cons(Nil(),Nil()))))
        - Weak TRS:
            f[Ite][False][Ite](False(),Cons(x,xs),y) -> f(xs,Cons(Cons(Nil(),Nil()),y))
            f[Ite][False][Ite](True(),x',Cons(x,xs)) -> f(x',xs)
            g[Ite][False][Ite](False(),Cons(x,xs),y) -> g(xs,Cons(Cons(Nil(),Nil()),y))
            g[Ite][False][Ite](True(),x',Cons(x,xs)) -> g(x',xs)
        - Signature:
            {f/2,f[Ite][False][Ite]/3,g/2,g[Ite][False][Ite]/3,goal/2,lt0/2,notEmpty/1,number4/1} / {Cons/2,False/0
            ,Nil/0,True/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,f[Ite][False][Ite],g,g[Ite][False][Ite],goal,lt0
            ,notEmpty,number4} and constructors {Cons,False,Nil,True}
    + Applied Processor:
        Ara {araHeuristics = NoHeuristics, minDegree = 1, maxDegree = 2, araTimeout = 5, araRuleShifting = Nothing}
    + Details:
        Signatures used:
        ----------------
          Cons :: ["A"(0) x "A"(4)] -(4)-> "A"(4)

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