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

WORST_CASE(Omega(n^1),?)