/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:
            double(0()) -> 0()
            double(s(x)) -> s(s(double(x)))
            minus(x,0()) -> x
            minus(s(x),s(y)) -> minus(x,y)
            plus(0(),y) -> y
            plus(s(x),y) -> plus(x,s(y))
            plus(s(x),y) -> s(plus(x,y))
            plus(s(x),y) -> s(plus(minus(x,y),double(y)))
        - Signature:
            {double/1,minus/2,plus/2} / {0/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {double,minus,plus} and constructors {0,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)))
            minus(x,0()) -> x
            minus(s(x),s(y)) -> minus(x,y)
            plus(0(),y) -> y
            plus(s(x),y) -> plus(x,s(y))
            plus(s(x),y) -> s(plus(x,y))
            plus(s(x),y) -> s(plus(minus(x,y),double(y)))
        - Signature:
            {double/1,minus/2,plus/2} / {0/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {double,minus,plus} and constructors {0,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)))
            minus(x,0()) -> x
            minus(s(x),s(y)) -> minus(x,y)
            plus(0(),y) -> y
            plus(s(x),y) -> plus(x,s(y))
            plus(s(x),y) -> s(plus(x,y))
            plus(s(x),y) -> s(plus(minus(x,y),double(y)))
        - Signature:
            {double/1,minus/2,plus/2} / {0/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {double,minus,plus} and constructors {0,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),?)