/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:
            double(0()) -> 0()
            double(s(x)) -> s(s(double(x)))
            greater(x,0()) -> first()
            greater(0(),s(y)) -> second()
            greater(s(x),s(y)) -> greater(x,y)
            if(false(),x,y,z) -> true()
            if(first(),x,y,z) -> if(le(s(x),y,s(z)),s(x),y,s(z))
            if(second(),x,y,z) -> if(le(s(x),s(y),z),s(x),s(y),z)
            le(0(),y,z) -> greater(y,z)
            le(s(x),0(),z) -> false()
            le(s(x),s(y),0()) -> false()
            le(s(x),s(y),s(z)) -> le(x,y,z)
            triple(x) -> if(le(x,x,double(x)),x,0(),0())
        - Signature:
            {double/1,greater/2,if/4,le/3,triple/1} / {0/0,false/0,first/0,s/1,second/0,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {double,greater,if,le,triple} and constructors {0,false,first,s
            ,second,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            double(0()) -> 0()
            double(s(x)) -> s(s(double(x)))
            greater(x,0()) -> first()
            greater(0(),s(y)) -> second()
            greater(s(x),s(y)) -> greater(x,y)
            if(false(),x,y,z) -> true()
            if(first(),x,y,z) -> if(le(s(x),y,s(z)),s(x),y,s(z))
            if(second(),x,y,z) -> if(le(s(x),s(y),z),s(x),s(y),z)
            le(0(),y,z) -> greater(y,z)
            le(s(x),0(),z) -> false()
            le(s(x),s(y),0()) -> false()
            le(s(x),s(y),s(z)) -> le(x,y,z)
            triple(x) -> if(le(x,x,double(x)),x,0(),0())
        - Signature:
            {double/1,greater/2,if/4,le/3,triple/1} / {0/0,false/0,first/0,s/1,second/0,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {double,greater,if,le,triple} and constructors {0,false,first,s
            ,second,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            double(0()) -> 0()
            double(s(x)) -> s(s(double(x)))
            greater(x,0()) -> first()
            greater(0(),s(y)) -> second()
            greater(s(x),s(y)) -> greater(x,y)
            if(false(),x,y,z) -> true()
            if(first(),x,y,z) -> if(le(s(x),y,s(z)),s(x),y,s(z))
            if(second(),x,y,z) -> if(le(s(x),s(y),z),s(x),s(y),z)
            le(0(),y,z) -> greater(y,z)
            le(s(x),0(),z) -> false()
            le(s(x),s(y),0()) -> false()
            le(s(x),s(y),s(z)) -> le(x,y,z)
            triple(x) -> if(le(x,x,double(x)),x,0(),0())
        - Signature:
            {double/1,greater/2,if/4,le/3,triple/1} / {0/0,false/0,first/0,s/1,second/0,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {double,greater,if,le,triple} and constructors {0,false,first,s
            ,second,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),?)