/export/starexec/sandbox2/solver/bin/starexec_run_tct_rci /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(0(),x2) -> 0()
            f(S(x),0()) -> 0()
            f(S(x'),S(x)) -> h(g(x',S(x)),f(S(S(x')),x))
            g(0(),x2) -> 0()
            g(S(x),0()) -> 0()
            g(S(x),S(x')) -> h(f(S(x),S(x')),g(x,S(S(x'))))
            h(0(),0()) -> 0()
            h(0(),S(x)) -> h(0(),x)
            h(S(x),x2) -> h(x,x2)
        - Signature:
            {f/2,g/2,h/2} / {0/0,S/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,g,h} and constructors {0,S}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            f(0(),x2) -> 0()
            f(S(x),0()) -> 0()
            f(S(x'),S(x)) -> h(g(x',S(x)),f(S(S(x')),x))
            g(0(),x2) -> 0()
            g(S(x),0()) -> 0()
            g(S(x),S(x')) -> h(f(S(x),S(x')),g(x,S(S(x'))))
            h(0(),0()) -> 0()
            h(0(),S(x)) -> h(0(),x)
            h(S(x),x2) -> h(x,x2)
        - Signature:
            {f/2,g/2,h/2} / {0/0,S/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,g,h} and constructors {0,S}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          f(S(x),y){y -> S(y)} =
            f(S(x),S(y)) ->^+ h(g(x,S(y)),f(S(S(x)),y))
              = C[f(S(S(x)),y) = f(S(x),y){x -> S(x)}]

WORST_CASE(Omega(n^1),?)