/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:
            aver(sum,z) -> if(gt(sum,double(z)),sum,z)
            average(x,y) -> aver(plus(x,y),0())
            double(0()) -> 0()
            double(s(x)) -> s(s(double(x)))
            gt(0(),y) -> false()
            gt(s(x),0()) -> true()
            gt(s(x),s(y)) -> gt(x,y)
            if(false(),sum,z) -> z
            if(true(),sum,z) -> aver(sum,s(z))
            plus(0(),y) -> y
            plus(s(x),y) -> s(plus(x,y))
        - Signature:
            {aver/2,average/2,double/1,gt/2,if/3,plus/2} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {aver,average,double,gt,if,plus} and constructors {0,false,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            aver(sum,z) -> if(gt(sum,double(z)),sum,z)
            average(x,y) -> aver(plus(x,y),0())
            double(0()) -> 0()
            double(s(x)) -> s(s(double(x)))
            gt(0(),y) -> false()
            gt(s(x),0()) -> true()
            gt(s(x),s(y)) -> gt(x,y)
            if(false(),sum,z) -> z
            if(true(),sum,z) -> aver(sum,s(z))
            plus(0(),y) -> y
            plus(s(x),y) -> s(plus(x,y))
        - Signature:
            {aver/2,average/2,double/1,gt/2,if/3,plus/2} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {aver,average,double,gt,if,plus} and constructors {0,false,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            aver(sum,z) -> if(gt(sum,double(z)),sum,z)
            average(x,y) -> aver(plus(x,y),0())
            double(0()) -> 0()
            double(s(x)) -> s(s(double(x)))
            gt(0(),y) -> false()
            gt(s(x),0()) -> true()
            gt(s(x),s(y)) -> gt(x,y)
            if(false(),sum,z) -> z
            if(true(),sum,z) -> aver(sum,s(z))
            plus(0(),y) -> y
            plus(s(x),y) -> s(plus(x,y))
        - Signature:
            {aver/2,average/2,double/1,gt/2,if/3,plus/2} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {aver,average,double,gt,if,plus} and constructors {0,false,s,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          double(x){x -> s(x)} =
            double(s(x)) ->^+ s(s(double(x)))
              = C[double(x) = double(x){}]

WORST_CASE(Omega(n^1),?)