/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(NON_POLY,?)
* Step 1: Sum.  WORST_CASE(NON_POLY,?)
    + Considered Problem:
        - Strict TRS:
            greaters(x,.(y,z)) -> if(<=(y,x),greaters(x,z),.(y,greaters(x,z)))
            greaters(x,nil()) -> nil()
            lowers(x,.(y,z)) -> if(<=(y,x),.(y,lowers(x,z)),lowers(x,z))
            lowers(x,nil()) -> nil()
            qsort(.(x,y)) -> ++(qsort(lowers(x,y)),.(x,qsort(greaters(x,y))))
            qsort(nil()) -> nil()
        - Signature:
            {greaters/2,lowers/2,qsort/1} / {++/2,./2,<=/2,if/3,nil/0}
        - Obligation:
             runtime complexity wrt. defined symbols {greaters,lowers,qsort} and constructors {++,.,<=,if,nil}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(NON_POLY,?)
    + Considered Problem:
        - Strict TRS:
            greaters(x,.(y,z)) -> if(<=(y,x),greaters(x,z),.(y,greaters(x,z)))
            greaters(x,nil()) -> nil()
            lowers(x,.(y,z)) -> if(<=(y,x),.(y,lowers(x,z)),lowers(x,z))
            lowers(x,nil()) -> nil()
            qsort(.(x,y)) -> ++(qsort(lowers(x,y)),.(x,qsort(greaters(x,y))))
            qsort(nil()) -> nil()
        - Signature:
            {greaters/2,lowers/2,qsort/1} / {++/2,./2,<=/2,if/3,nil/0}
        - Obligation:
             runtime complexity wrt. defined symbols {greaters,lowers,qsort} and constructors {++,.,<=,if,nil}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(NON_POLY,?)
    + Considered Problem:
        - Strict TRS:
            greaters(x,.(y,z)) -> if(<=(y,x),greaters(x,z),.(y,greaters(x,z)))
            greaters(x,nil()) -> nil()
            lowers(x,.(y,z)) -> if(<=(y,x),.(y,lowers(x,z)),lowers(x,z))
            lowers(x,nil()) -> nil()
            qsort(.(x,y)) -> ++(qsort(lowers(x,y)),.(x,qsort(greaters(x,y))))
            qsort(nil()) -> nil()
        - Signature:
            {greaters/2,lowers/2,qsort/1} / {++/2,./2,<=/2,if/3,nil/0}
        - Obligation:
             runtime complexity wrt. defined symbols {greaters,lowers,qsort} and constructors {++,.,<=,if,nil}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          greaters(x,z){z -> .(y,z)} =
            greaters(x,.(y,z)) ->^+ if(<=(y,x),greaters(x,z),.(y,greaters(x,z)))
              = C[greaters(x,z) = greaters(x,z){}]
          greaters(x,z){z -> .(y,z)} =
            greaters(x,.(y,z)) ->^+ if(<=(y,x),greaters(x,z),.(y,greaters(x,z)))
              = C[greaters(x,z) = greaters(x,z){}]

WORST_CASE(NON_POLY,?)