Runti Compl Inner Rewri 22807 pair #381904249

details

property	value
status	timeout (wallclock)
benchmark	qsort.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
space	AProVE_09_Inductive

run statistics

property	value
solver	tct 2018-07-13
configuration	tct_rci
runtime (wallclock)	294.881250143 seconds
cpu usage	1200.60110547
max memory	3.56263936E9

stage attributes

unavailable

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),?)
* Step 1: Sum WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            append(cons(x,xs),ys()) -> cons(x,append(xs,ys()))
            append(nil(),ys()) -> ys()
            filterhigh(n,cons(x,xs)) -> if2(ge(x,n),n,x,xs)
            filterhigh(n,nil()) -> nil()
            filterlow(n,cons(x,xs)) -> if1(ge(n,x),n,x,xs)
            filterlow(n,nil()) -> nil()
            ge(x,0()) -> true()
            ge(0(),s(x)) -> false()
            ge(s(x),s(y)) -> ge(x,y)
            if1(false(),n,x,xs) -> cons(x,filterlow(n,xs))
            if1(true(),n,x,xs) -> filterlow(n,xs)
            if2(false(),n,x,xs) -> cons(x,filterhigh(n,xs))
            if2(true(),n,x,xs) -> filterhigh(n,xs)
            qsort(cons(x,xs)) -> append(qsort(filterlow(x,cons(x,xs))),cons(x,qsort(filterhigh(x,cons(x,xs)))))
            qsort(nil()) -> nil()
        - Signature:
            {append/2,filterhigh/2,filterlow/2,ge/2,if1/4,if2/4,qsort/1} / {0/0,cons/2,false/0,nil/0,s/1,true/0,ys/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {append,filterhigh,filterlow,ge,if1,if2
            ,qsort} and constructors {0,cons,false,nil,s,true,ys}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            append(cons(x,xs),ys()) -> cons(x,append(xs,ys()))
            append(nil(),ys()) -> ys()
            filterhigh(n,cons(x,xs)) -> if2(ge(x,n),n,x,xs)
            filterhigh(n,nil()) -> nil()
            filterlow(n,cons(x,xs)) -> if1(ge(n,x),n,x,xs)
            filterlow(n,nil()) -> nil()
            ge(x,0()) -> true()
            ge(0(),s(x)) -> false()
            ge(s(x),s(y)) -> ge(x,y)
            if1(false(),n,x,xs) -> cons(x,filterlow(n,xs))
            if1(true(),n,x,xs) -> filterlow(n,xs)
            if2(false(),n,x,xs) -> cons(x,filterhigh(n,xs))
            if2(true(),n,x,xs) -> filterhigh(n,xs)
            qsort(cons(x,xs)) -> append(qsort(filterlow(x,cons(x,xs))),cons(x,qsort(filterhigh(x,cons(x,xs)))))
            qsort(nil()) -> nil()
        - Signature:
            {append/2,filterhigh/2,filterlow/2,ge/2,if1/4,if2/4,qsort/1} / {0/0,cons/2,false/0,nil/0,s/1,true/0,ys/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {append,filterhigh,filterlow,ge,if1,if2
            ,qsort} and constructors {0,cons,false,nil,s,true,ys}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          append(y,ys()){y -> cons(x,y)} =
            append(cons(x,y),ys()) ->^+ cons(x,append(y,ys()))
              = C[append(y,ys()) = append(y,ys()){}]

WORST_CASE(Omega(n^1),?)

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