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

** Step 1.b:1: Bounds.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            f(f(x)) -> f(c(f(x)))
            f(f(x)) -> f(d(f(x)))
            g(c(x)) -> x
            g(c(1())) -> g(d(h(0())))
            g(c(h(0()))) -> g(d(1()))
            g(d(x)) -> x
            g(h(x)) -> g(x)
        - Signature:
            {f/1,g/1} / {0/0,1/0,c/1,d/1,h/1}
        - Obligation:
             runtime complexity wrt. defined symbols {f,g} and constructors {0,1,c,d,h}
    + Applied Processor:
        Bounds {initialAutomaton = minimal, enrichment = match}
    + Details:
        The problem is match-bounded by 1.
        The enriched problem is compatible with follwoing automaton.
          0_0() -> 1
          0_0() -> 2
          0_1() -> 5
          1_0() -> 1
          1_0() -> 2
          1_1() -> 1
          1_1() -> 4
          c_0(2) -> 1
          c_0(2) -> 2
          d_0(2) -> 1
          d_0(2) -> 2
          d_1(4) -> 3
          f_0(2) -> 1
          g_0(2) -> 1
          g_1(2) -> 1
          g_1(3) -> 1
          h_0(2) -> 1
          h_0(2) -> 2
          h_1(5) -> 1
          h_1(5) -> 4
          2 -> 1
          4 -> 1
** Step 1.b:2: EmptyProcessor.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            f(f(x)) -> f(c(f(x)))
            f(f(x)) -> f(d(f(x)))
            g(c(x)) -> x
            g(c(1())) -> g(d(h(0())))
            g(c(h(0()))) -> g(d(1()))
            g(d(x)) -> x
            g(h(x)) -> g(x)
        - Signature:
            {f/1,g/1} / {0/0,1/0,c/1,d/1,h/1}
        - Obligation:
             runtime complexity wrt. defined symbols {f,g} and constructors {0,1,c,d,h}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(Omega(n^1),O(n^1))