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

** Step 1.b:1: Bounds.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            active(c()) -> mark(d())
            active(g(X)) -> mark(h(X))
            active(h(d())) -> mark(g(c()))
            g(ok(X)) -> ok(g(X))
            h(ok(X)) -> ok(h(X))
            proper(c()) -> ok(c())
            proper(d()) -> ok(d())
            proper(g(X)) -> g(proper(X))
            proper(h(X)) -> h(proper(X))
            top(mark(X)) -> top(proper(X))
            top(ok(X)) -> top(active(X))
        - Signature:
            {active/1,g/1,h/1,proper/1,top/1} / {c/0,d/0,mark/1,ok/1}
        - Obligation:
             runtime complexity wrt. defined symbols {active,g,h,proper,top} and constructors {c,d,mark,ok}
    + Applied Processor:
        Bounds {initialAutomaton = perSymbol, enrichment = match}
    + Details:
        The problem is match-bounded by 4.
        The enriched problem is compatible with follwoing automaton.
          active_0(2) -> 1
          active_0(3) -> 1
          active_0(6) -> 1
          active_0(7) -> 1
          active_1(2) -> 14
          active_1(3) -> 14
          active_1(6) -> 14
          active_1(7) -> 14
          active_2(10) -> 15
          active_2(13) -> 15
          active_3(16) -> 17
          active_4(18) -> 19
          c_0() -> 2
          c_1() -> 13
          d_0() -> 3
          d_1() -> 10
          d_2() -> 16
          d_3() -> 18
          g_0(2) -> 4
          g_0(3) -> 4
          g_0(6) -> 4
          g_0(7) -> 4
          g_1(2) -> 11
          g_1(3) -> 11
          g_1(6) -> 11
          g_1(7) -> 11
          h_0(2) -> 5
          h_0(3) -> 5
          h_0(6) -> 5
          h_0(7) -> 5
          h_1(2) -> 12
          h_1(3) -> 12
          h_1(6) -> 12
          h_1(7) -> 12
          mark_0(2) -> 6
          mark_0(3) -> 6
          mark_0(6) -> 6
          mark_0(7) -> 6
          mark_1(10) -> 1
          mark_1(10) -> 14
          mark_2(16) -> 15
          ok_0(2) -> 7
          ok_0(3) -> 7
          ok_0(6) -> 7
          ok_0(7) -> 7
          ok_1(10) -> 8
          ok_1(10) -> 14
          ok_1(11) -> 4
          ok_1(11) -> 11
          ok_1(12) -> 5
          ok_1(12) -> 12
          ok_1(13) -> 8
          ok_1(13) -> 14
          ok_2(16) -> 15
          ok_3(18) -> 17
          proper_0(2) -> 8
          proper_0(3) -> 8
          proper_0(6) -> 8
          proper_0(7) -> 8
          proper_1(2) -> 14
          proper_1(3) -> 14
          proper_1(6) -> 14
          proper_1(7) -> 14
          proper_2(10) -> 15
          proper_3(16) -> 17
          top_0(2) -> 9
          top_0(3) -> 9
          top_0(6) -> 9
          top_0(7) -> 9
          top_1(14) -> 9
          top_2(15) -> 9
          top_3(17) -> 9
          top_4(19) -> 9
** Step 1.b:2: EmptyProcessor.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            active(c()) -> mark(d())
            active(g(X)) -> mark(h(X))
            active(h(d())) -> mark(g(c()))
            g(ok(X)) -> ok(g(X))
            h(ok(X)) -> ok(h(X))
            proper(c()) -> ok(c())
            proper(d()) -> ok(d())
            proper(g(X)) -> g(proper(X))
            proper(h(X)) -> h(proper(X))
            top(mark(X)) -> top(proper(X))
            top(ok(X)) -> top(active(X))
        - Signature:
            {active/1,g/1,h/1,proper/1,top/1} / {c/0,d/0,mark/1,ok/1}
        - Obligation:
             runtime complexity wrt. defined symbols {active,g,h,proper,top} and constructors {c,d,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))