Runti Compl Full Rewri 10127 pair #381902144

details

property	value
status	complete
benchmark	t011.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	HirokawaMiddeldorp_04

run statistics

property	value
solver	tct 2018-07-13
configuration	tct_rc
runtime (wallclock)	0.192691802979 seconds
cpu usage	0.701383801
max memory	3.8526976E7

stage attributes

key	value
output-size	7982
starexec-result	WORST_CASE(Omega(n^1),O(n^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(Omega(n^1),O(n^1))
* Step 1: Sum WORST_CASE(Omega(n^1),O(n^1))
    + Considered Problem:
        - Strict TRS:
            g(f(x),y) -> f(h(x,y))
            h(x,y) -> g(x,f(y))
        - Signature:
            {g/2,h/2} / {f/1}
        - Obligation:
             runtime complexity wrt. defined symbols {g,h} and constructors {f}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            g(f(x),y) -> f(h(x,y))
            h(x,y) -> g(x,f(y))
        - Signature:
            {g/2,h/2} / {f/1}
        - Obligation:
             runtime complexity wrt. defined symbols {g,h} and constructors {f}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          g(x,z){x -> f(x)} =
            g(f(x),z) ->^+ f(g(x,f(z)))
              = C[g(x,f(z)) = g(x,z){z -> f(z)}]

** Step 1.b:1: ToInnermost WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            g(f(x),y) -> f(h(x,y))
            h(x,y) -> g(x,f(y))
        - Signature:
            {g/2,h/2} / {f/1}
        - Obligation:
             runtime complexity wrt. defined symbols {g,h} and constructors {f}
    + Applied Processor:
        ToInnermost
    + Details:
        switch to innermost, as the system is overlay and right linear and does not contain weak rules
** Step 1.b:2: DependencyPairs WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            g(f(x),y) -> f(h(x,y))
            h(x,y) -> g(x,f(y))
        - Signature:
            {g/2,h/2} / {f/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {g,h} and constructors {f}
    + Applied Processor:
        DependencyPairs {dpKind_ = WIDP}
    + Details:
        We add the following weak innermost dependency pairs:
        
        Strict DPs
          g#(f(x),y) -> c_1(h#(x,y))
          h#(x,y) -> c_2(g#(x,f(y)))
        Weak DPs
          
        
        and mark the set of starting terms.
** Step 1.b:3: UsableRules WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            g#(f(x),y) -> c_1(h#(x,y))
            h#(x,y) -> c_2(g#(x,f(y)))
        - Strict TRS:
            g(f(x),y) -> f(h(x,y))
            h(x,y) -> g(x,f(y))
        - Signature:
            {g/2,h/2,g#/2,h#/2} / {f/1,c_1/1,c_2/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {g#,h#} and constructors {f}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          g#(f(x),y) -> c_1(h#(x,y))
          h#(x,y) -> c_2(g#(x,f(y)))
** Step 1.b:4: PredecessorEstimationCP WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            g#(f(x),y) -> c_1(h#(x,y))
            h#(x,y) -> c_2(g#(x,f(y)))
        - Signature:
            {g/2,h/2,g#/2,h#/2} / {f/1,c_1/1,c_2/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {g#,h#} and constructors {f}
    + Applied Processor:
        PredecessorEstimationCP {onSelectionCP = any intersect of rules of CDG leaf and strict-rules, withComplexityPair = NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing}}

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