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

WORST_CASE(Omega(n^1),?)