Runti Compl Full Rewri 10127 pair #381902197

details

property	value
status	complete
benchmark	06.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	Der95

run statistics

property	value
solver	tct 2018-07-13
configuration	tct_rc
runtime (wallclock)	0.0140738487244 seconds
cpu usage	0.020949443
max memory	3014656.0

stage attributes

key	value
output-size	2894
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)) -> g(g(f(x)))
            f(g(x)) -> g(g(g(x)))
        - Signature:
            {f/1} / {g/1}
        - Obligation:
             runtime complexity wrt. defined symbols {f} and constructors {g}
    + 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)) -> g(g(f(x)))
            f(g(x)) -> g(g(g(x)))
        - Signature:
            {f/1} / {g/1}
        - Obligation:
             runtime complexity wrt. defined symbols {f} and constructors {g}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          f(x){x -> g(x)} =
            f(g(x)) ->^+ g(g(f(x)))
              = C[f(x) = f(x){}]

** Step 1.b:1: ToInnermost WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            f(g(x)) -> g(g(f(x)))
            f(g(x)) -> g(g(g(x)))
        - Signature:
            {f/1} / {g/1}
        - Obligation:
             runtime complexity wrt. defined symbols {f} and constructors {g}
    + 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: Bounds WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            f(g(x)) -> g(g(f(x)))
            f(g(x)) -> g(g(g(x)))
        - Signature:
            {f/1} / {g/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f} and constructors {g}
    + Applied Processor:
        Bounds {initialAutomaton = perSymbol, enrichment = match}
    + Details:
        The problem is match-bounded by 1.
        The enriched problem is compatible with follwoing automaton.
          f_0(2) -> 1
          f_1(2) -> 4
          g_0(2) -> 2
          g_1(2) -> 4
          g_1(3) -> 1
          g_1(3) -> 4
          g_1(4) -> 3
** Step 1.b:3: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            f(g(x)) -> g(g(f(x)))
            f(g(x)) -> g(g(g(x)))
        - Signature:
            {f/1} / {g/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f} and constructors {g}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(Omega(n^1),O(n^1))

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