/export/starexec/sandbox/solver/bin/starexec_run_tct_rc /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


--------------------------------------------------------------------------------


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: 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 = perSymbol, enrichment = match}
    + Details:
        The problem is match-bounded by 6.
        The enriched problem is compatible with follwoing automaton.
          active_0(2) -> 1
          active_0(5) -> 1
          active_0(6) -> 1
          active_1(2) -> 14
          active_1(5) -> 14
          active_1(6) -> 14
          active_2(11) -> 15
          active_3(26) -> 21
          active_4(29) -> 30
          active_5(27) -> 33
          active_6(36) -> 37
          c_0() -> 2
          c_1() -> 11
          c_2() -> 18
          c_3() -> 25
          c_4() -> 35
          f_0(2) -> 3
          f_0(5) -> 3
          f_0(6) -> 3
          f_1(2) -> 12
          f_1(5) -> 12
          f_1(6) -> 12
          f_1(10) -> 9
          f_2(17) -> 16
          f_2(19) -> 15
          f_3(22) -> 21
          f_3(24) -> 26
          f_4(27) -> 29
          g_0(2) -> 4
          g_0(5) -> 4
          g_0(6) -> 4
          g_1(2) -> 13
          g_1(5) -> 13
          g_1(6) -> 13
          g_1(11) -> 10
          g_2(18) -> 17
          g_2(20) -> 19
          g_3(18) -> 24
          g_3(23) -> 22
          g_4(18) -> 28
          g_4(25) -> 27
          g_5(25) -> 31
          g_5(32) -> 30
          g_5(35) -> 36
          g_6(34) -> 33
          mark_0(2) -> 5
          mark_0(5) -> 5
          mark_0(6) -> 5
          mark_1(9) -> 1
          mark_1(9) -> 14
          mark_2(16) -> 15
          mark_4(28) -> 21
          mark_5(31) -> 30
          ok_0(2) -> 6
          ok_0(5) -> 6
          ok_0(6) -> 6
          ok_1(11) -> 7
          ok_1(11) -> 14
          ok_1(12) -> 3
          ok_1(12) -> 12
          ok_1(13) -> 4
          ok_1(13) -> 13
          ok_2(18) -> 20
          ok_3(24) -> 19
          ok_3(25) -> 23
          ok_3(25) -> 32
          ok_3(26) -> 15
          ok_4(27) -> 22
          ok_4(27) -> 30
          ok_4(29) -> 21
          ok_4(35) -> 34
          ok_5(36) -> 33
          proper_0(2) -> 7
          proper_0(5) -> 7
          proper_0(6) -> 7
          proper_1(2) -> 14
          proper_1(5) -> 14
          proper_1(6) -> 14
          proper_2(9) -> 15
          proper_2(10) -> 19
          proper_2(11) -> 20
          proper_3(16) -> 21
          proper_3(17) -> 22
          proper_3(18) -> 23
          proper_4(28) -> 30
          proper_5(18) -> 32
          proper_5(31) -> 33
          proper_6(25) -> 34
          top_0(2) -> 8
          top_0(5) -> 8
          top_0(6) -> 8
          top_1(14) -> 8
          top_2(15) -> 8
          top_3(21) -> 8
          top_4(30) -> 8
          top_5(33) -> 8
          top_6(37) -> 8
** 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))