Runti Compl Full Rewri 10127 pair #381902775

details

property	value
status	complete
benchmark	#3.53a.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n077.star.cs.uiowa.edu
space	AG01

run statistics

property	value
solver	tct 2018-07-13
configuration	tct_rc
runtime (wallclock)	0.176024198532 seconds
cpu usage	0.64749986
max memory	2.6632192E7

stage attributes

key	value
output-size	7185
starexec-result	WORST_CASE(?,O(1))

output

/export/starexec/sandbox/solver/bin/starexec_run_tct_rc /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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WORST_CASE(?,O(1))
* Step 1: Sum WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict TRS:
            f(s(x),y,y) -> f(y,x,s(x))
            g(x,y) -> x
            g(x,y) -> y
        - Signature:
            {f/3,g/2} / {s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {f,g} and constructors {s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: DependencyPairs WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict TRS:
            f(s(x),y,y) -> f(y,x,s(x))
            g(x,y) -> x
            g(x,y) -> y
        - Signature:
            {f/3,g/2} / {s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {f,g} and constructors {s}
    + Applied Processor:
        DependencyPairs {dpKind_ = WIDP}
    + Details:
        We add the following weak dependency pairs:
        
        Strict DPs
          f#(s(x),y,y) -> c_1(f#(y,x,s(x)))
          g#(x,y) -> c_2(x)
          g#(x,y) -> c_3(y)
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 3: UsableRules WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            f#(s(x),y,y) -> c_1(f#(y,x,s(x)))
            g#(x,y) -> c_2(x)
            g#(x,y) -> c_3(y)
        - Strict TRS:
            f(s(x),y,y) -> f(y,x,s(x))
            g(x,y) -> x
            g(x,y) -> y
        - Signature:
            {f/3,g/2,f#/3,g#/2} / {s/1,c_1/1,c_2/1,c_3/1}
        - Obligation:
             runtime complexity wrt. defined symbols {f#,g#} and constructors {s}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          f#(s(x),y,y) -> c_1(f#(y,x,s(x)))
          g#(x,y) -> c_2(x)
          g#(x,y) -> c_3(y)
* Step 4: PredecessorEstimationCP WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            f#(s(x),y,y) -> c_1(f#(y,x,s(x)))
            g#(x,y) -> c_2(x)
            g#(x,y) -> c_3(y)
        - Signature:
            {f/3,g/2,f#/3,g#/2} / {s/1,c_1/1,c_2/1,c_3/1}
        - Obligation:
             runtime complexity wrt. defined symbols {f#,g#} and constructors {s}
    + Applied Processor:
        PredecessorEstimationCP {onSelectionCP = any intersect of rules of CDG leaf and strict-rules, withComplexityPair = NaturalMI {miDimension = 1, miDegree = 0, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing}}
    + Details:
        We first use the processor NaturalMI {miDimension = 1, miDegree = 0, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing} to orient following rules strictly:
          1: f#(s(x),y,y) -> c_1(f#(y,x,s(x)))
          2: g#(x,y) -> c_2(x)
          3: g#(x,y) -> c_3(y)
          
        The strictly oriented rules are moved into the weak component.
** Step 4.a:1: NaturalMI WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            f#(s(x),y,y) -> c_1(f#(y,x,s(x)))
            g#(x,y) -> c_2(x)
            g#(x,y) -> c_3(y)
        - Signature:
            {f/3,g/2,f#/3,g#/2} / {s/1,c_1/1,c_2/1,c_3/1}
        - Obligation:
             runtime complexity wrt. defined symbols {f#,g#} and constructors {s}
    + Applied Processor:
        NaturalMI {miDimension = 1, miDegree = 0, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just first alternative for predecessorEstimation on any intersect of rules of CDG leaf and strict-rules}
    + Details:
        We apply a matrix interpretation of kind constructor based matrix interpretation (containing no more than 0 non-zero interpretation-entries in the diagonal of the component-wise maxima):
        The following argument positions are considered usable:
          none

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