Runti Compl Inner Rewri 22807 pair #381905001

details

property	value
status	complete
benchmark	select.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_Glenstrup

run statistics

property	value
solver	tct 2018-07-13
configuration	tct_rci
runtime (wallclock)	2.42054986954 seconds
cpu usage	9.793762269
max memory	9.484288E7

stage attributes

key	value
output-size	25213
starexec-result	WORST_CASE(Omega(n^1),O(n^2))

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^2))
* Step 1: Sum WORST_CASE(Omega(n^1),O(n^2))
    + Considered Problem:
        - Strict TRS:
            revapp(Cons(x,xs),rest) -> revapp(xs,Cons(x,rest))
            revapp(Nil(),rest) -> rest
            select(Cons(x,xs)) -> selects(x,Nil(),xs)
            select(Nil()) -> Nil()
            selects(x,revprefix,Nil()) -> Cons(Cons(x,revapp(revprefix,Nil())),Nil())
            selects(x',revprefix,Cons(x,xs)) -> Cons(Cons(x',revapp(revprefix,Cons(x,xs)))
                                                    ,selects(x,Cons(x',revprefix),xs))
        - Signature:
            {revapp/2,select/1,selects/3} / {Cons/2,Nil/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {revapp,select,selects} and constructors {Cons,Nil}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            revapp(Cons(x,xs),rest) -> revapp(xs,Cons(x,rest))
            revapp(Nil(),rest) -> rest
            select(Cons(x,xs)) -> selects(x,Nil(),xs)
            select(Nil()) -> Nil()
            selects(x,revprefix,Nil()) -> Cons(Cons(x,revapp(revprefix,Nil())),Nil())
            selects(x',revprefix,Cons(x,xs)) -> Cons(Cons(x',revapp(revprefix,Cons(x,xs)))
                                                    ,selects(x,Cons(x',revprefix),xs))
        - Signature:
            {revapp/2,select/1,selects/3} / {Cons/2,Nil/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {revapp,select,selects} and constructors {Cons,Nil}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          revapp(y,z){y -> Cons(x,y)} =
            revapp(Cons(x,y),z) ->^+ revapp(y,Cons(x,z))
              = C[revapp(y,Cons(x,z)) = revapp(y,z){z -> Cons(x,z)}]

** Step 1.b:1: DependencyPairs WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict TRS:
            revapp(Cons(x,xs),rest) -> revapp(xs,Cons(x,rest))
            revapp(Nil(),rest) -> rest
            select(Cons(x,xs)) -> selects(x,Nil(),xs)
            select(Nil()) -> Nil()
            selects(x,revprefix,Nil()) -> Cons(Cons(x,revapp(revprefix,Nil())),Nil())
            selects(x',revprefix,Cons(x,xs)) -> Cons(Cons(x',revapp(revprefix,Cons(x,xs)))
                                                    ,selects(x,Cons(x',revprefix),xs))
        - Signature:
            {revapp/2,select/1,selects/3} / {Cons/2,Nil/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {revapp,select,selects} and constructors {Cons,Nil}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          revapp#(Cons(x,xs),rest) -> c_1(revapp#(xs,Cons(x,rest)))
          revapp#(Nil(),rest) -> c_2()
          select#(Cons(x,xs)) -> c_3(selects#(x,Nil(),xs))
          select#(Nil()) -> c_4()
          selects#(x,revprefix,Nil()) -> c_5(revapp#(revprefix,Nil()))
          selects#(x',revprefix,Cons(x,xs)) -> c_6(revapp#(revprefix,Cons(x,xs)),selects#(x,Cons(x',revprefix),xs))
        Weak DPs
          
        
        and mark the set of starting terms.
** Step 1.b:2: PredecessorEstimation WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict DPs:
            revapp#(Cons(x,xs),rest) -> c_1(revapp#(xs,Cons(x,rest)))
            revapp#(Nil(),rest) -> c_2()
            select#(Cons(x,xs)) -> c_3(selects#(x,Nil(),xs))
            select#(Nil()) -> c_4()
            selects#(x,revprefix,Nil()) -> c_5(revapp#(revprefix,Nil()))
            selects#(x',revprefix,Cons(x,xs)) -> c_6(revapp#(revprefix,Cons(x,xs)),selects#(x,Cons(x',revprefix),xs))
        - Weak TRS:
            revapp(Cons(x,xs),rest) -> revapp(xs,Cons(x,rest))
            revapp(Nil(),rest) -> rest
            select(Cons(x,xs)) -> selects(x,Nil(),xs)
            select(Nil()) -> Nil()
            selects(x,revprefix,Nil()) -> Cons(Cons(x,revapp(revprefix,Nil())),Nil())
            selects(x',revprefix,Cons(x,xs)) -> Cons(Cons(x',revapp(revprefix,Cons(x,xs)))
                                                    ,selects(x,Cons(x',revprefix),xs))
        - Signature:
            {revapp/2,select/1,selects/3,revapp#/2,select#/1,selects#/3} / {Cons/2,Nil/0,c_1/1,c_2/0,c_3/1,c_4/0,c_5/1
            ,c_6/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {revapp#,select#,selects#} and constructors {Cons,Nil}
    + Applied Processor:

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