/export/starexec/sandbox/solver/bin/starexec_run_tct_rc /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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WORST_CASE(Omega(n^1),?)
* Step 1: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            cond(false(),x,y) -> double(log(x,square(s(s(y)))))
            cond(true(),x,y) -> s(0())
            double(0()) -> 0()
            double(s(x)) -> s(s(double(x)))
            le(0(),v) -> true()
            le(s(u),0()) -> false()
            le(s(u),s(v)) -> le(u,v)
            log(x,s(s(y))) -> cond(le(x,s(s(y))),x,y)
            plus(n,0()) -> n
            plus(n,s(m)) -> s(plus(n,m))
            square(0()) -> 0()
            square(s(x)) -> s(plus(square(x),double(x)))
        - Signature:
            {cond/3,double/1,le/2,log/2,plus/2,square/1} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {cond,double,le,log,plus,square} 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:
            cond(false(),x,y) -> double(log(x,square(s(s(y)))))
            cond(true(),x,y) -> s(0())
            double(0()) -> 0()
            double(s(x)) -> s(s(double(x)))
            le(0(),v) -> true()
            le(s(u),0()) -> false()
            le(s(u),s(v)) -> le(u,v)
            log(x,s(s(y))) -> cond(le(x,s(s(y))),x,y)
            plus(n,0()) -> n
            plus(n,s(m)) -> s(plus(n,m))
            square(0()) -> 0()
            square(s(x)) -> s(plus(square(x),double(x)))
        - Signature:
            {cond/3,double/1,le/2,log/2,plus/2,square/1} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {cond,double,le,log,plus,square} 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:
            cond(false(),x,y) -> double(log(x,square(s(s(y)))))
            cond(true(),x,y) -> s(0())
            double(0()) -> 0()
            double(s(x)) -> s(s(double(x)))
            le(0(),v) -> true()
            le(s(u),0()) -> false()
            le(s(u),s(v)) -> le(u,v)
            log(x,s(s(y))) -> cond(le(x,s(s(y))),x,y)
            plus(n,0()) -> n
            plus(n,s(m)) -> s(plus(n,m))
            square(0()) -> 0()
            square(s(x)) -> s(plus(square(x),double(x)))
        - Signature:
            {cond/3,double/1,le/2,log/2,plus/2,square/1} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {cond,double,le,log,plus,square} 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),?)