/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:
            and(x,false()) -> false()
            and(x,true()) -> x
            double(0()) -> 0()
            double(s(x)) -> s(s(double(x)))
            f(true(),x,y) -> f(and(gt(x,y),gt(y,s(s(0())))),plus(s(0()),x),double(y))
            gt(0(),v) -> false()
            gt(s(u),0()) -> true()
            gt(s(u),s(v)) -> gt(u,v)
            plus(n,0()) -> n
            plus(n,s(m)) -> s(plus(n,m))
        - Signature:
            {and/2,double/1,f/3,gt/2,plus/2} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {and,double,f,gt,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:
            and(x,false()) -> false()
            and(x,true()) -> x
            double(0()) -> 0()
            double(s(x)) -> s(s(double(x)))
            f(true(),x,y) -> f(and(gt(x,y),gt(y,s(s(0())))),plus(s(0()),x),double(y))
            gt(0(),v) -> false()
            gt(s(u),0()) -> true()
            gt(s(u),s(v)) -> gt(u,v)
            plus(n,0()) -> n
            plus(n,s(m)) -> s(plus(n,m))
        - Signature:
            {and/2,double/1,f/3,gt/2,plus/2} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {and,double,f,gt,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:
            and(x,false()) -> false()
            and(x,true()) -> x
            double(0()) -> 0()
            double(s(x)) -> s(s(double(x)))
            f(true(),x,y) -> f(and(gt(x,y),gt(y,s(s(0())))),plus(s(0()),x),double(y))
            gt(0(),v) -> false()
            gt(s(u),0()) -> true()
            gt(s(u),s(v)) -> gt(u,v)
            plus(n,0()) -> n
            plus(n,s(m)) -> s(plus(n,m))
        - Signature:
            {and/2,double/1,f/3,gt/2,plus/2} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {and,double,f,gt,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),?)