Runti Compl Full Rewri 10127 pair #381902158

details

property	value
status	complete
benchmark	jwmatchb2.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n038.star.cs.uiowa.edu
space	Waldmann_06

run statistics

property	value
solver	tct 2018-07-13
configuration	tct_rc
runtime (wallclock)	0.0352578163147 seconds
cpu usage	0.087456484
max memory	1.0706944E7

stage attributes

key	value
output-size	3034
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:
            h(f(x,y)) -> f(f(a(),h(h(y))),x)
        - Signature:
            {h/1} / {a/0,f/2}
        - Obligation:
             runtime complexity wrt. defined symbols {h} and constructors {a,f}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            h(f(x,y)) -> f(f(a(),h(h(y))),x)
        - Signature:
            {h/1} / {a/0,f/2}
        - Obligation:
             runtime complexity wrt. defined symbols {h} and constructors {a,f}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          h(y){y -> f(x,y)} =
            h(f(x,y)) ->^+ f(f(a(),h(h(y))),x)
              = C[h(y) = h(y){}]

** Step 1.b:1: ToInnermost WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            h(f(x,y)) -> f(f(a(),h(h(y))),x)
        - Signature:
            {h/1} / {a/0,f/2}
        - Obligation:
             runtime complexity wrt. defined symbols {h} and constructors {a,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: Bounds WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            h(f(x,y)) -> f(f(a(),h(h(y))),x)
        - Signature:
            {h/1} / {a/0,f/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {h} and constructors {a,f}
    + Applied Processor:
        Bounds {initialAutomaton = minimal, enrichment = match}
    + Details:
        The problem is match-bounded by 2.
        The enriched problem is compatible with follwoing automaton.
          a_0() -> 2
          a_1() -> 4
          a_2() -> 8
          f_0(2,2) -> 2
          f_1(3,2) -> 1
          f_1(3,2) -> 6
          f_1(3,2) -> 10
          f_1(4,5) -> 3
          f_2(7,3) -> 5
          f_2(7,3) -> 9
          f_2(8,9) -> 7
          h_0(2) -> 1
          h_1(2) -> 6
          h_1(6) -> 5
          h_2(2) -> 10
          h_2(10) -> 9
** Step 1.b:3: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            h(f(x,y)) -> f(f(a(),h(h(y))),x)
        - Signature:
            {h/1} / {a/0,f/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {h} and constructors {a,f}
    + 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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