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


--------------------------------------------------------------------------------


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)))
            exp(0()) -> s(0())
            exp(s(x)) -> double(exp(x))
            f(a(),0(),y) -> y
            f(a(),s(x),y) -> f(b(),y,s(x))
            f(b(),y,x) -> f(a(),half(x),exp(y))
            half(0()) -> double(0())
            half(s(0())) -> half(0())
            half(s(s(x))) -> s(half(x))
            tower(x) -> f(a(),x,s(0()))
        - Signature:
            {double/1,exp/1,f/3,half/1,tower/1} / {0/0,a/0,b/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {double,exp,f,half,tower} and constructors {0,a,b,s}
    + 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)))
            exp(0()) -> s(0())
            exp(s(x)) -> double(exp(x))
            f(a(),0(),y) -> y
            f(a(),s(x),y) -> f(b(),y,s(x))
            f(b(),y,x) -> f(a(),half(x),exp(y))
            half(0()) -> double(0())
            half(s(0())) -> half(0())
            half(s(s(x))) -> s(half(x))
            tower(x) -> f(a(),x,s(0()))
        - Signature:
            {double/1,exp/1,f/3,half/1,tower/1} / {0/0,a/0,b/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {double,exp,f,half,tower} and constructors {0,a,b,s}
    + 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)))
            exp(0()) -> s(0())
            exp(s(x)) -> double(exp(x))
            f(a(),0(),y) -> y
            f(a(),s(x),y) -> f(b(),y,s(x))
            f(b(),y,x) -> f(a(),half(x),exp(y))
            half(0()) -> double(0())
            half(s(0())) -> half(0())
            half(s(s(x))) -> s(half(x))
            tower(x) -> f(a(),x,s(0()))
        - Signature:
            {double/1,exp/1,f/3,half/1,tower/1} / {0/0,a/0,b/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {double,exp,f,half,tower} and constructors {0,a,b,s}
    + 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),?)