Runti Compl Inner Rewri 22807 pair #381904397

details

property	value
status	complete
benchmark	subtrees.raml.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n074.star.cs.uiowa.edu
space	raML

run statistics

property	value
solver	tct 2018-07-13
configuration	tct_rci
runtime (wallclock)	5.94033384323 seconds
cpu usage	22.770910201
max memory	1.61697792E8

stage attributes

key	value
output-size	59941
starexec-result	WORST_CASE(?,O(n^2))

output

/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(?,O(n^2))
* Step 1: Sum WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict TRS:
            append(@l1,@l2) -> append#1(@l1,@l2)
            append#1(::(@x,@xs),@l2) -> ::(@x,append(@xs,@l2))
            append#1(nil(),@l2) -> @l2
            subtrees(@t) -> subtrees#1(@t)
            subtrees#1(leaf()) -> nil()
            subtrees#1(node(@x,@t1,@t2)) -> subtrees#2(subtrees(@t1),@t1,@t2,@x)
            subtrees#2(@l1,@t1,@t2,@x) -> subtrees#3(subtrees(@t2),@l1,@t1,@t2,@x)
            subtrees#3(@l2,@l1,@t1,@t2,@x) -> ::(node(@x,@t1,@t2),append(@l1,@l2))
        - Signature:
            {append/2,append#1/2,subtrees/1,subtrees#1/1,subtrees#2/4,subtrees#3/5} / {::/2,leaf/0,nil/0,node/3}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {append,append#1,subtrees,subtrees#1,subtrees#2
            ,subtrees#3} and constructors {::,leaf,nil,node}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: DependencyPairs WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict TRS:
            append(@l1,@l2) -> append#1(@l1,@l2)
            append#1(::(@x,@xs),@l2) -> ::(@x,append(@xs,@l2))
            append#1(nil(),@l2) -> @l2
            subtrees(@t) -> subtrees#1(@t)
            subtrees#1(leaf()) -> nil()
            subtrees#1(node(@x,@t1,@t2)) -> subtrees#2(subtrees(@t1),@t1,@t2,@x)
            subtrees#2(@l1,@t1,@t2,@x) -> subtrees#3(subtrees(@t2),@l1,@t1,@t2,@x)
            subtrees#3(@l2,@l1,@t1,@t2,@x) -> ::(node(@x,@t1,@t2),append(@l1,@l2))
        - Signature:
            {append/2,append#1/2,subtrees/1,subtrees#1/1,subtrees#2/4,subtrees#3/5} / {::/2,leaf/0,nil/0,node/3}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {append,append#1,subtrees,subtrees#1,subtrees#2
            ,subtrees#3} and constructors {::,leaf,nil,node}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          append#(@l1,@l2) -> c_1(append#1#(@l1,@l2))
          append#1#(::(@x,@xs),@l2) -> c_2(append#(@xs,@l2))
          append#1#(nil(),@l2) -> c_3()
          subtrees#(@t) -> c_4(subtrees#1#(@t))
          subtrees#1#(leaf()) -> c_5()
          subtrees#1#(node(@x,@t1,@t2)) -> c_6(subtrees#2#(subtrees(@t1),@t1,@t2,@x),subtrees#(@t1))
          subtrees#2#(@l1,@t1,@t2,@x) -> c_7(subtrees#3#(subtrees(@t2),@l1,@t1,@t2,@x),subtrees#(@t2))
          subtrees#3#(@l2,@l1,@t1,@t2,@x) -> c_8(append#(@l1,@l2))
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 3: PredecessorEstimation WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict DPs:
            append#(@l1,@l2) -> c_1(append#1#(@l1,@l2))
            append#1#(::(@x,@xs),@l2) -> c_2(append#(@xs,@l2))
            append#1#(nil(),@l2) -> c_3()
            subtrees#(@t) -> c_4(subtrees#1#(@t))
            subtrees#1#(leaf()) -> c_5()
            subtrees#1#(node(@x,@t1,@t2)) -> c_6(subtrees#2#(subtrees(@t1),@t1,@t2,@x),subtrees#(@t1))
            subtrees#2#(@l1,@t1,@t2,@x) -> c_7(subtrees#3#(subtrees(@t2),@l1,@t1,@t2,@x),subtrees#(@t2))
            subtrees#3#(@l2,@l1,@t1,@t2,@x) -> c_8(append#(@l1,@l2))
        - Weak TRS:
            append(@l1,@l2) -> append#1(@l1,@l2)
            append#1(::(@x,@xs),@l2) -> ::(@x,append(@xs,@l2))
            append#1(nil(),@l2) -> @l2
            subtrees(@t) -> subtrees#1(@t)
            subtrees#1(leaf()) -> nil()
            subtrees#1(node(@x,@t1,@t2)) -> subtrees#2(subtrees(@t1),@t1,@t2,@x)
            subtrees#2(@l1,@t1,@t2,@x) -> subtrees#3(subtrees(@t2),@l1,@t1,@t2,@x)
            subtrees#3(@l2,@l1,@t1,@t2,@x) -> ::(node(@x,@t1,@t2),append(@l1,@l2))
        - Signature:
            {append/2,append#1/2,subtrees/1,subtrees#1/1,subtrees#2/4,subtrees#3/5,append#/2,append#1#/2,subtrees#/1
            ,subtrees#1#/1,subtrees#2#/4,subtrees#3#/5} / {::/2,leaf/0,nil/0,node/3,c_1/1,c_2/1,c_3/0,c_4/1,c_5/0,c_6/2
            ,c_7/2,c_8/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {append#,append#1#,subtrees#,subtrees#1#,subtrees#2#
            ,subtrees#3#} and constructors {::,leaf,nil,node}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {3,5}
        by application of
          Pre({3,5}) = {1,4}.
        Here rules are labelled as follows:
          1: append#(@l1,@l2) -> c_1(append#1#(@l1,@l2))
          2: append#1#(::(@x,@xs),@l2) -> c_2(append#(@xs,@l2))
          3: append#1#(nil(),@l2) -> c_3()
          4: subtrees#(@t) -> c_4(subtrees#1#(@t))

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