/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(c()) -> mark(f(g(c())))
            active(f(g(X))) -> mark(g(X))
            f(ok(X)) -> ok(f(X))
            g(ok(X)) -> ok(g(X))
            proper(c()) -> ok(c())
            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} / {c/0,mark/1,ok/1}
        - Obligation:
             runtime complexity wrt. defined symbols {active,f,g,proper,top} and constructors {c,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(c()) -> mark(f(g(c())))
            active(f(g(X))) -> mark(g(X))
            f(ok(X)) -> ok(f(X))
            g(ok(X)) -> ok(g(X))
            proper(c()) -> ok(c())
            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} / {c/0,mark/1,ok/1}
        - Obligation:
             runtime complexity wrt. defined symbols {active,f,g,proper,top} and constructors {c,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(c()) -> mark(f(g(c())))
            active(f(g(X))) -> mark(g(X))
            f(ok(X)) -> ok(f(X))
            g(ok(X)) -> ok(g(X))
            proper(c()) -> ok(c())
            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} / {c/0,mark/1,ok/1}
        - Obligation:
             runtime complexity wrt. defined symbols {active,f,g,proper,top} and constructors {c,mark,ok}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          f(x){x -> ok(x)} =
            f(ok(x)) ->^+ ok(f(x))
              = C[f(x) = f(x){}]

** Step 1.b:1: Bounds.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            active(c()) -> mark(f(g(c())))
            active(f(g(X))) -> mark(g(X))
            f(ok(X)) -> ok(f(X))
            g(ok(X)) -> ok(g(X))
            proper(c()) -> ok(c())
            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} / {c/0,mark/1,ok/1}
        - Obligation:
             runtime complexity wrt. defined symbols {active,f,g,proper,top} and constructors {c,mark,ok}
    + Applied Processor:
        Bounds {initialAutomaton = minimal, enrichment = match}
    + Details:
        The problem is match-bounded by 6.
        The enriched problem is compatible with follwoing automaton.
          active_0(2) -> 1
          active_1(2) -> 7
          active_2(5) -> 8
          active_3(19) -> 14
          active_4(22) -> 23
          active_5(20) -> 26
          active_6(29) -> 30
          c_0() -> 2
          c_1() -> 5
          c_2() -> 11
          c_3() -> 18
          c_4() -> 28
          f_0(2) -> 1
          f_1(2) -> 6
          f_1(4) -> 3
          f_2(10) -> 9
          f_2(12) -> 8
          f_3(15) -> 14
          f_3(17) -> 19
          f_4(20) -> 22
          g_0(2) -> 1
          g_1(2) -> 6
          g_1(5) -> 4
          g_2(11) -> 10
          g_2(13) -> 12
          g_3(11) -> 17
          g_3(16) -> 15
          g_4(11) -> 21
          g_4(18) -> 20
          g_5(18) -> 24
          g_5(25) -> 23
          g_5(28) -> 29
          g_6(27) -> 26
          mark_0(2) -> 2
          mark_1(3) -> 1
          mark_1(3) -> 7
          mark_2(9) -> 8
          mark_4(21) -> 14
          mark_5(24) -> 23
          ok_0(2) -> 2
          ok_1(5) -> 1
          ok_1(5) -> 7
          ok_1(6) -> 1
          ok_1(6) -> 6
          ok_2(11) -> 13
          ok_3(17) -> 12
          ok_3(18) -> 16
          ok_3(18) -> 25
          ok_3(19) -> 8
          ok_4(20) -> 15
          ok_4(20) -> 23
          ok_4(22) -> 14
          ok_4(28) -> 27
          ok_5(29) -> 26
          proper_0(2) -> 1
          proper_1(2) -> 7
          proper_2(3) -> 8
          proper_2(4) -> 12
          proper_2(5) -> 13
          proper_3(9) -> 14
          proper_3(10) -> 15
          proper_3(11) -> 16
          proper_4(21) -> 23
          proper_5(11) -> 25
          proper_5(24) -> 26
          proper_6(18) -> 27
          top_0(2) -> 1
          top_1(7) -> 1
          top_2(8) -> 1
          top_3(14) -> 1
          top_4(23) -> 1
          top_5(26) -> 1
          top_6(30) -> 1
** Step 1.b:2: EmptyProcessor.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            active(c()) -> mark(f(g(c())))
            active(f(g(X))) -> mark(g(X))
            f(ok(X)) -> ok(f(X))
            g(ok(X)) -> ok(g(X))
            proper(c()) -> ok(c())
            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} / {c/0,mark/1,ok/1}
        - Obligation:
             runtime complexity wrt. defined symbols {active,f,g,proper,top} and constructors {c,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))