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

** Step 1.b:1: ToInnermost.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            a() -> n__a()
            activate(X) -> X
            activate(n__a()) -> a()
            activate(n__f(X)) -> f(X)
            activate(n__g(X)) -> g(activate(X))
            f(X) -> n__f(X)
            f(n__f(n__a())) -> f(n__g(n__f(n__a())))
            g(X) -> n__g(X)
        - Signature:
            {a/0,activate/1,f/1,g/1} / {n__a/0,n__f/1,n__g/1}
        - Obligation:
             runtime complexity wrt. defined symbols {a,activate,f,g} and constructors {n__a,n__f,n__g}
    + Applied Processor:
        ToInnermost
    + Details:
        switch to innermost, as the system is overlay and right linear and does not contain weak rules
** Step 1.b:2: Bounds.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            a() -> n__a()
            activate(X) -> X
            activate(n__a()) -> a()
            activate(n__f(X)) -> f(X)
            activate(n__g(X)) -> g(activate(X))
            f(X) -> n__f(X)
            f(n__f(n__a())) -> f(n__g(n__f(n__a())))
            g(X) -> n__g(X)
        - Signature:
            {a/0,activate/1,f/1,g/1} / {n__a/0,n__f/1,n__g/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a,activate,f,g} and constructors {n__a,n__f,n__g}
    + Applied Processor:
        Bounds {initialAutomaton = minimal, enrichment = match}
    + Details:
        The problem is match-bounded by 3.
        The enriched problem is compatible with follwoing automaton.
          a_0() -> 1
          a_1() -> 1
          a_1() -> 3
          activate_0(2) -> 1
          activate_1(2) -> 3
          activate_1(4) -> 3
          activate_2(4) -> 5
          f_0(2) -> 1
          f_1(2) -> 1
          f_1(2) -> 3
          f_1(3) -> 5
          f_2(1) -> 3
          f_2(1) -> 5
          g_0(2) -> 1
          g_1(3) -> 1
          g_1(3) -> 3
          g_2(5) -> 3
          n__a_0() -> 1
          n__a_0() -> 2
          n__a_0() -> 3
          n__a_1() -> 1
          n__a_2() -> 1
          n__a_2() -> 3
          n__f_0(2) -> 1
          n__f_0(2) -> 2
          n__f_0(2) -> 3
          n__f_1(1) -> 3
          n__f_1(1) -> 4
          n__f_1(1) -> 5
          n__f_1(2) -> 1
          n__f_2(2) -> 1
          n__f_2(2) -> 3
          n__f_2(3) -> 5
          n__f_3(1) -> 3
          n__f_3(1) -> 5
          n__g_0(2) -> 1
          n__g_0(2) -> 2
          n__g_0(2) -> 3
          n__g_1(2) -> 1
          n__g_1(4) -> 1
          n__g_1(4) -> 2
          n__g_1(4) -> 3
          n__g_2(3) -> 1
          n__g_2(3) -> 3
          n__g_2(5) -> 1
          n__g_3(5) -> 3
          2 -> 1
          2 -> 3
          4 -> 3
          4 -> 5
** Step 1.b:3: EmptyProcessor.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            a() -> n__a()
            activate(X) -> X
            activate(n__a()) -> a()
            activate(n__f(X)) -> f(X)
            activate(n__g(X)) -> g(activate(X))
            f(X) -> n__f(X)
            f(n__f(n__a())) -> f(n__g(n__f(n__a())))
            g(X) -> n__g(X)
        - Signature:
            {a/0,activate/1,f/1,g/1} / {n__a/0,n__f/1,n__g/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a,activate,f,g} and constructors {n__a,n__f,n__g}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

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