/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:
            10() -> double(s(double(s(s(0())))))
            1024() -> 1024_1(0())
            1024_1(x) -> if(lt(x,10()),x)
            double(0()) -> 0()
            double(s(x)) -> s(s(double(x)))
            if(false(),x) -> s(0())
            if(true(),x) -> double(1024_1(s(x)))
            lt(x,0()) -> false()
            lt(0(),s(y)) -> true()
            lt(s(x),s(y)) -> lt(x,y)
        - Signature:
            {10/0,1024/0,1024_1/1,double/1,if/2,lt/2} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {10,1024,1024_1,double,if,lt} 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:
            10() -> double(s(double(s(s(0())))))
            1024() -> 1024_1(0())
            1024_1(x) -> if(lt(x,10()),x)
            double(0()) -> 0()
            double(s(x)) -> s(s(double(x)))
            if(false(),x) -> s(0())
            if(true(),x) -> double(1024_1(s(x)))
            lt(x,0()) -> false()
            lt(0(),s(y)) -> true()
            lt(s(x),s(y)) -> lt(x,y)
        - Signature:
            {10/0,1024/0,1024_1/1,double/1,if/2,lt/2} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {10,1024,1024_1,double,if,lt} 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:
            10() -> double(s(double(s(s(0())))))
            1024() -> 1024_1(0())
            1024_1(x) -> if(lt(x,10()),x)
            double(0()) -> 0()
            double(s(x)) -> s(s(double(x)))
            if(false(),x) -> s(0())
            if(true(),x) -> double(1024_1(s(x)))
            lt(x,0()) -> false()
            lt(0(),s(y)) -> true()
            lt(s(x),s(y)) -> lt(x,y)
        - Signature:
            {10/0,1024/0,1024_1/1,double/1,if/2,lt/2} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {10,1024,1024_1,double,if,lt} 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),?)