/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),?)
* Step 1: Sum WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            +(0(),y) -> y
            +(s(x),y) -> s(+(x,y))
            ++(:(x,xs),ys) -> :(x,++(xs,ys))
            ++(nil(),ys) -> ys
            -(x,0()) -> x
            -(0(),s(y)) -> 0()
            -(s(x),s(y)) -> -(x,y)
            avg(xs) -> quot(hd(sum(xs)),length(xs))
            hd(:(x,xs)) -> x
            length(:(x,xs)) -> s(length(xs))
            length(nil()) -> 0()
            quot(0(),s(y)) -> 0()
            quot(s(x),s(y)) -> s(quot(-(x,y),s(y)))
            sum(++(xs,:(x,:(y,ys)))) -> sum(++(xs,sum(:(x,:(y,ys)))))
            sum(:(x,:(y,xs))) -> sum(:(+(x,y),xs))
            sum(:(x,nil())) -> :(x,nil())
        - Signature:
            {+/2,++/2,-/2,avg/1,hd/1,length/1,quot/2,sum/1} / {0/0,:/2,nil/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {+,++,-,avg,hd,length,quot,sum} and constructors {0,:,nil,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            +(0(),y) -> y
            +(s(x),y) -> s(+(x,y))
            ++(:(x,xs),ys) -> :(x,++(xs,ys))
            ++(nil(),ys) -> ys
            -(x,0()) -> x
            -(0(),s(y)) -> 0()
            -(s(x),s(y)) -> -(x,y)
            avg(xs) -> quot(hd(sum(xs)),length(xs))
            hd(:(x,xs)) -> x
            length(:(x,xs)) -> s(length(xs))
            length(nil()) -> 0()
            quot(0(),s(y)) -> 0()
            quot(s(x),s(y)) -> s(quot(-(x,y),s(y)))
            sum(++(xs,:(x,:(y,ys)))) -> sum(++(xs,sum(:(x,:(y,ys)))))
            sum(:(x,:(y,xs))) -> sum(:(+(x,y),xs))
            sum(:(x,nil())) -> :(x,nil())
        - Signature:
            {+/2,++/2,-/2,avg/1,hd/1,length/1,quot/2,sum/1} / {0/0,:/2,nil/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {+,++,-,avg,hd,length,quot,sum} and constructors {0,:,nil,s}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          +(x,y){x -> s(x)} =
            +(s(x),y) ->^+ s(+(x,y))
              = C[+(x,y) = +(x,y){}]

WORST_CASE(Omega(n^1),?)