Runti Compl Full Rewri 10127 pair #381902147

details

property	value
status	complete
benchmark	27.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n028.star.cs.uiowa.edu
space	Der95

run statistics

property	value
solver	tct 2018-07-13
configuration	tct_rc
runtime (wallclock)	0.0462491512299 seconds
cpu usage	0.149131591
max memory	1.6990208E7

stage attributes

key	value
output-size	2938
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(x,y) -> h(x,y)
            h(f(x),y) -> f(g(x,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(x,y) -> h(x,y)
            h(f(x),y) -> f(g(x,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,z))
              = C[g(x,z) = g(x,z){}]

** Step 1.b:1: ToInnermost WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            g(x,y) -> h(x,y)
            h(f(x),y) -> f(g(x,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: Bounds WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            g(x,y) -> h(x,y)
            h(f(x),y) -> f(g(x,y))
        - Signature:
            {g/2,h/2} / {f/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {g,h} and constructors {f}
    + Applied Processor:
        Bounds {initialAutomaton = minimal, enrichment = match}
    + Details:
        The problem is match-bounded by 2.
        The enriched problem is compatible with follwoing automaton.
          f_0(2) -> 2
          f_1(3) -> 1
          f_1(3) -> 3
          g_0(2,2) -> 1
          g_1(2,2) -> 3
          h_0(2,2) -> 1
          h_1(2,2) -> 1
          h_2(2,2) -> 3
** Step 1.b:3: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            g(x,y) -> h(x,y)
            h(f(x),y) -> f(g(x,y))
        - Signature:
            {g/2,h/2} / {f/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {g,h} and constructors {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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