/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:
            f(x,0(),0()) -> s(x)
            f(0(),y,0()) -> s(y)
            f(0(),0(),z) -> s(z)
            f(0(),s(0()),s(0())) -> s(s(0()))
            f(0(),s(0()),s(s(z))) -> f(0(),s(0()),z)
            f(0(),s(s(y)),s(0())) -> f(0(),y,s(0()))
            f(0(),s(s(y)),s(s(z))) -> f(0(),y,f(0(),s(s(y)),s(z)))
            f(s(x),0(),s(z)) -> f(x,s(0()),z)
            f(s(x),s(y),0()) -> f(x,y,s(0()))
            f(s(x),s(y),s(z)) -> f(x,y,f(s(x),s(y),z))
            f(s(0()),y,z) -> f(0(),s(y),s(z))
        - Signature:
            {f/3} / {0/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {f} 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(x,0(),0()) -> s(x)
            f(0(),y,0()) -> s(y)
            f(0(),0(),z) -> s(z)
            f(0(),s(0()),s(0())) -> s(s(0()))
            f(0(),s(0()),s(s(z))) -> f(0(),s(0()),z)
            f(0(),s(s(y)),s(0())) -> f(0(),y,s(0()))
            f(0(),s(s(y)),s(s(z))) -> f(0(),y,f(0(),s(s(y)),s(z)))
            f(s(x),0(),s(z)) -> f(x,s(0()),z)
            f(s(x),s(y),0()) -> f(x,y,s(0()))
            f(s(x),s(y),s(z)) -> f(x,y,f(s(x),s(y),z))
            f(s(0()),y,z) -> f(0(),s(y),s(z))
        - Signature:
            {f/3} / {0/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {f} 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(x,0(),0()) -> s(x)
            f(0(),y,0()) -> s(y)
            f(0(),0(),z) -> s(z)
            f(0(),s(0()),s(0())) -> s(s(0()))
            f(0(),s(0()),s(s(z))) -> f(0(),s(0()),z)
            f(0(),s(s(y)),s(0())) -> f(0(),y,s(0()))
            f(0(),s(s(y)),s(s(z))) -> f(0(),y,f(0(),s(s(y)),s(z)))
            f(s(x),0(),s(z)) -> f(x,s(0()),z)
            f(s(x),s(y),0()) -> f(x,y,s(0()))
            f(s(x),s(y),s(z)) -> f(x,y,f(s(x),s(y),z))
            f(s(0()),y,z) -> f(0(),s(y),s(z))
        - Signature:
            {f/3} / {0/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {f} and constructors {0,s}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          f(0(),s(0()),x){x -> s(s(x))} =
            f(0(),s(0()),s(s(x))) ->^+ f(0(),s(0()),x)
              = C[f(0(),s(0()),x) = f(0(),s(0()),x){}]

WORST_CASE(Omega(n^1),?)