/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(?,O(n^1))
* Step 1: Sum.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            f(a()) -> g(h(a()))
            h(g(x)) -> g(h(f(x)))
            k(x,h(x),a()) -> h(x)
            k(f(x),y,x) -> f(x)
        - Signature:
            {f/1,h/1,k/3} / {a/0,g/1}
        - Obligation:
             runtime complexity wrt. defined symbols {f,h,k} and constructors {a,g}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Bounds.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            f(a()) -> g(h(a()))
            h(g(x)) -> g(h(f(x)))
            k(x,h(x),a()) -> h(x)
            k(f(x),y,x) -> f(x)
        - Signature:
            {f/1,h/1,k/3} / {a/0,g/1}
        - Obligation:
             runtime complexity wrt. defined symbols {f,h,k} and constructors {a,g}
    + Applied Processor:
        Bounds {initialAutomaton = perSymbol, enrichment = match}
    + Details:
        The problem is match-bounded by 2.
        The enriched problem is compatible with follwoing automaton.
          a_0() -> 1
          a_1() -> 7
          f_0(1) -> 2
          f_0(3) -> 2
          f_1(1) -> 9
          f_1(3) -> 9
          f_2(6) -> 11
          g_0(1) -> 3
          g_0(3) -> 3
          g_1(6) -> 2
          g_1(6) -> 9
          g_1(8) -> 4
          g_2(10) -> 8
          h_0(1) -> 4
          h_0(3) -> 4
          h_1(7) -> 6
          h_1(9) -> 8
          h_2(11) -> 10
          k_0(1,1,1) -> 5
          k_0(1,1,3) -> 5
          k_0(1,3,1) -> 5
          k_0(1,3,3) -> 5
          k_0(3,1,1) -> 5
          k_0(3,1,3) -> 5
          k_0(3,3,1) -> 5
          k_0(3,3,3) -> 5
* Step 3: EmptyProcessor.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            f(a()) -> g(h(a()))
            h(g(x)) -> g(h(f(x)))
            k(x,h(x),a()) -> h(x)
            k(f(x),y,x) -> f(x)
        - Signature:
            {f/1,h/1,k/3} / {a/0,g/1}
        - Obligation:
             runtime complexity wrt. defined symbols {f,h,k} and constructors {a,g}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))