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

WORST_CASE(Omega(n^1),?)