Runti Compl Inner Rewri 22807 pair #381904774

details

property	value
status	complete
benchmark	4.30.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n035.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	tct 2018-07-13
configuration	tct_rci
runtime (wallclock)	6.48728680611 seconds
cpu usage	19.053193043
max memory	1.05046016E8

stage attributes

key	value
output-size	3588
starexec-result	WORST_CASE(Omega(n^1),O(n^1))

output

/export/starexec/sandbox/solver/bin/starexec_run_tct_rci /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:
            f(.(.(x,y),z)) -> f(.(x,.(y,z)))
            f(.(nil(),y)) -> .(nil(),f(y))
            f(nil()) -> nil()
            g(.(x,.(y,z))) -> g(.(.(x,y),z))
            g(.(x,nil())) -> .(g(x),nil())
            g(nil()) -> nil()
        - Signature:
            {f/1,g/1} / {./2,nil/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,g} and constructors {.,nil}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            f(.(.(x,y),z)) -> f(.(x,.(y,z)))
            f(.(nil(),y)) -> .(nil(),f(y))
            f(nil()) -> nil()
            g(.(x,.(y,z))) -> g(.(.(x,y),z))
            g(.(x,nil())) -> .(g(x),nil())
            g(nil()) -> nil()
        - Signature:
            {f/1,g/1} / {./2,nil/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,g} and constructors {.,nil}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          f(.(x,z)){x -> .(x,y)} =
            f(.(.(x,y),z)) ->^+ f(.(x,.(y,z)))
              = C[f(.(x,.(y,z))) = f(.(x,z)){z -> .(y,z)}]

** Step 1.b:1: Bounds WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            f(.(.(x,y),z)) -> f(.(x,.(y,z)))
            f(.(nil(),y)) -> .(nil(),f(y))
            f(nil()) -> nil()
            g(.(x,.(y,z))) -> g(.(.(x,y),z))
            g(.(x,nil())) -> .(g(x),nil())
            g(nil()) -> nil()
        - Signature:
            {f/1,g/1} / {./2,nil/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,g} and constructors {.,nil}
    + Applied Processor:
        Bounds {initialAutomaton = minimal, enrichment = match}
    + Details:
        The problem is match-bounded by 1.
        The enriched problem is compatible with follwoing automaton.
          ._0(2,2) -> 2
          ._1(2,2) -> 4
          ._1(2,3) -> 3
          ._1(2,4) -> 3
          ._1(4,2) -> 7
          ._1(5,6) -> 1
          ._1(5,6) -> 5
          ._1(6,6) -> 6
          ._1(7,2) -> 7
          f_0(2) -> 1
          f_1(2) -> 6
          f_1(3) -> 1
          f_1(3) -> 6
          f_1(4) -> 6
          g_0(2) -> 1
          g_1(2) -> 5
          g_1(4) -> 5
          g_1(7) -> 1
          g_1(7) -> 5
          nil_0() -> 2
          nil_1() -> 1
          nil_1() -> 5
          nil_1() -> 6
** Step 1.b:2: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            f(.(.(x,y),z)) -> f(.(x,.(y,z)))
            f(.(nil(),y)) -> .(nil(),f(y))
            f(nil()) -> nil()
            g(.(x,.(y,z))) -> g(.(.(x,y),z))
            g(.(x,nil())) -> .(g(x),nil())
            g(nil()) -> nil()
        - Signature:
            {f/1,g/1} / {./2,nil/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,g} and constructors {.,nil}
    + Applied Processor:

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