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

** Step 1.b:1: Bounds.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            active(f(X)) -> f(active(X))
            active(f(f(a()))) -> mark(f(g(f(a()))))
            f(mark(X)) -> mark(f(X))
            f(ok(X)) -> ok(f(X))
            g(ok(X)) -> ok(g(X))
            proper(a()) -> ok(a())
            proper(f(X)) -> f(proper(X))
            proper(g(X)) -> g(proper(X))
            top(mark(X)) -> top(proper(X))
            top(ok(X)) -> top(active(X))
        - Signature:
            {active/1,f/1,g/1,proper/1,top/1} / {a/0,mark/1,ok/1}
        - Obligation:
             runtime complexity wrt. defined symbols {active,f,g,proper,top} and constructors {a,mark,ok}
    + Applied Processor:
        Bounds {initialAutomaton = minimal, enrichment = match}
    + Details:
        The problem is match-bounded by 2.
        The enriched problem is compatible with follwoing automaton.
          a_0() -> 2
          a_1() -> 3
          active_0(2) -> 1
          active_1(2) -> 4
          active_2(2) -> 6
          active_2(3) -> 5
          f_0(2) -> 1
          f_1(2) -> 3
          f_2(6) -> 5
          g_0(2) -> 1
          g_1(2) -> 3
          mark_0(2) -> 2
          mark_1(3) -> 1
          mark_1(3) -> 3
          ok_0(2) -> 2
          ok_1(3) -> 1
          ok_1(3) -> 3
          ok_1(3) -> 4
          proper_0(2) -> 1
          proper_1(2) -> 4
          top_0(2) -> 1
          top_1(4) -> 1
          top_2(5) -> 1
** Step 1.b:2: EmptyProcessor.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            active(f(X)) -> f(active(X))
            active(f(f(a()))) -> mark(f(g(f(a()))))
            f(mark(X)) -> mark(f(X))
            f(ok(X)) -> ok(f(X))
            g(ok(X)) -> ok(g(X))
            proper(a()) -> ok(a())
            proper(f(X)) -> f(proper(X))
            proper(g(X)) -> g(proper(X))
            top(mark(X)) -> top(proper(X))
            top(ok(X)) -> top(active(X))
        - Signature:
            {active/1,f/1,g/1,proper/1,top/1} / {a/0,mark/1,ok/1}
        - Obligation:
             runtime complexity wrt. defined symbols {active,f,g,proper,top} and constructors {a,mark,ok}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

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