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

WORST_CASE(Omega(n^1),?)