Runti Compl Full Rewri 10127 pair #381902925

details

property	value
status	complete
benchmark	#4.2.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n056.star.cs.uiowa.edu
space	Strategy_removed_AG01

run statistics

property	value
solver	tct 2018-07-13
configuration	tct_rc
runtime (wallclock)	0.0908210277557 seconds
cpu usage	0.36218418
max memory	2.889728E7

stage attributes

key	value
output-size	8292
starexec-result	WORST_CASE(Omega(n^1),O(n^1))

output

/export/starexec/sandbox2/solver/bin/starexec_run_tct_rc /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(g(x),s(0()),y) -> f(y,y,g(x))
            g(0()) -> 0()
            g(s(x)) -> s(g(x))
        - Signature:
            {f/3,g/1} / {0/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {f,g} and constructors {0,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            f(g(x),s(0()),y) -> f(y,y,g(x))
            g(0()) -> 0()
            g(s(x)) -> s(g(x))
        - Signature:
            {f/3,g/1} / {0/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {f,g} and constructors {0,s}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          g(x){x -> s(x)} =
            g(s(x)) ->^+ s(g(x))
              = C[g(x) = g(x){}]

** Step 1.b:1: DependencyPairs WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            f(g(x),s(0()),y) -> f(y,y,g(x))
            g(0()) -> 0()
            g(s(x)) -> s(g(x))
        - Signature:
            {f/3,g/1} / {0/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {f,g} and constructors {0,s}
    + Applied Processor:
        DependencyPairs {dpKind_ = WIDP}
    + Details:
        We add the following weak dependency pairs:
        
        Strict DPs
          f#(g(x),s(0()),y) -> c_1(f#(y,y,g(x)))
          g#(0()) -> c_2()
          g#(s(x)) -> c_3(g#(x))
        Weak DPs
          
        
        and mark the set of starting terms.
** Step 1.b:2: UsableRules WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            f#(g(x),s(0()),y) -> c_1(f#(y,y,g(x)))
            g#(0()) -> c_2()
            g#(s(x)) -> c_3(g#(x))
        - Strict TRS:
            f(g(x),s(0()),y) -> f(y,y,g(x))
            g(0()) -> 0()
            g(s(x)) -> s(g(x))
        - Signature:
            {f/3,g/1,f#/3,g#/1} / {0/0,s/1,c_1/1,c_2/0,c_3/1}
        - Obligation:
             runtime complexity wrt. defined symbols {f#,g#} and constructors {0,s}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          g#(0()) -> c_2()
          g#(s(x)) -> c_3(g#(x))
** Step 1.b:3: PredecessorEstimation WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            g#(0()) -> c_2()
            g#(s(x)) -> c_3(g#(x))
        - Signature:
            {f/3,g/1,f#/3,g#/1} / {0/0,s/1,c_1/1,c_2/0,c_3/1}
        - Obligation:
             runtime complexity wrt. defined symbols {f#,g#} and constructors {0,s}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1}
        by application of
          Pre({1}) = {2}.
        Here rules are labelled as follows:
          1: g#(0()) -> c_2()

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