/export/starexec/sandbox2/solver/bin/starexec_run_tct_rc /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/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)) -> mark(f(f(x)))
            chk(no(c())) -> active(c())
            chk(no(f(x))) -> f(chk(mat(f(f(f(f(f(f(f(f(f(f(X())))))))))),x)))
            f(active(x)) -> active(f(x))
            f(mark(x)) -> mark(f(x))
            f(no(x)) -> no(f(x))
            mat(f(x),c()) -> no(c())
            mat(f(x),f(y())) -> f(mat(x,y()))
            tp(mark(x)) -> tp(chk(mat(f(f(f(f(f(f(f(f(f(f(X())))))))))),x)))
        - Signature:
            {active/1,chk/1,f/1,mat/2,tp/1} / {X/0,c/0,mark/1,no/1,y/0}
        - Obligation:
             runtime complexity wrt. defined symbols {active,chk,f,mat,tp} and constructors {X,c,mark,no,y}
    + 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)) -> mark(f(f(x)))
            chk(no(c())) -> active(c())
            chk(no(f(x))) -> f(chk(mat(f(f(f(f(f(f(f(f(f(f(X())))))))))),x)))
            f(active(x)) -> active(f(x))
            f(mark(x)) -> mark(f(x))
            f(no(x)) -> no(f(x))
            mat(f(x),c()) -> no(c())
            mat(f(x),f(y())) -> f(mat(x,y()))
            tp(mark(x)) -> tp(chk(mat(f(f(f(f(f(f(f(f(f(f(X())))))))))),x)))
        - Signature:
            {active/1,chk/1,f/1,mat/2,tp/1} / {X/0,c/0,mark/1,no/1,y/0}
        - Obligation:
             runtime complexity wrt. defined symbols {active,chk,f,mat,tp} and constructors {X,c,mark,no,y}
    + 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)) -> mark(f(f(x)))
            chk(no(c())) -> active(c())
            chk(no(f(x))) -> f(chk(mat(f(f(f(f(f(f(f(f(f(f(X())))))))))),x)))
            f(active(x)) -> active(f(x))
            f(mark(x)) -> mark(f(x))
            f(no(x)) -> no(f(x))
            mat(f(x),c()) -> no(c())
            mat(f(x),f(y())) -> f(mat(x,y()))
            tp(mark(x)) -> tp(chk(mat(f(f(f(f(f(f(f(f(f(f(X())))))))))),x)))
        - Signature:
            {active/1,chk/1,f/1,mat/2,tp/1} / {X/0,c/0,mark/1,no/1,y/0}
        - Obligation:
             runtime complexity wrt. defined symbols {active,chk,f,mat,tp} and constructors {X,c,mark,no,y}
    + 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)) -> mark(f(f(x)))
            chk(no(c())) -> active(c())
            chk(no(f(x))) -> f(chk(mat(f(f(f(f(f(f(f(f(f(f(X())))))))))),x)))
            f(active(x)) -> active(f(x))
            f(mark(x)) -> mark(f(x))
            f(no(x)) -> no(f(x))
            mat(f(x),c()) -> no(c())
            mat(f(x),f(y())) -> f(mat(x,y()))
            tp(mark(x)) -> tp(chk(mat(f(f(f(f(f(f(f(f(f(f(X())))))))))),x)))
        - Signature:
            {active/1,chk/1,f/1,mat/2,tp/1} / {X/0,c/0,mark/1,no/1,y/0}
        - Obligation:
             runtime complexity wrt. defined symbols {active,chk,f,mat,tp} and constructors {X,c,mark,no,y}
    + Applied Processor:
        Bounds {initialAutomaton = minimal, enrichment = match}
    + Details:
        The problem is match-bounded by 2.
        The enriched problem is compatible with follwoing automaton.
          X_0() -> 2
          X_1() -> 17
          active_0(2) -> 1
          active_1(3) -> 1
          active_2(18) -> 5
          c_0() -> 2
          c_1() -> 3
          c_2() -> 18
          chk_0(2) -> 1
          chk_1(6) -> 5
          f_0(2) -> 1
          f_1(2) -> 4
          f_1(8) -> 7
          f_1(9) -> 8
          f_1(10) -> 9
          f_1(11) -> 10
          f_1(12) -> 11
          f_1(13) -> 12
          f_1(14) -> 13
          f_1(15) -> 14
          f_1(16) -> 15
          f_1(17) -> 16
          mark_0(2) -> 2
          mark_1(4) -> 1
          mark_1(4) -> 4
          mat_0(2,2) -> 1
          mat_1(7,2) -> 6
          no_0(2) -> 2
          no_1(3) -> 6
          no_1(4) -> 1
          no_1(4) -> 4
          tp_0(2) -> 1
          tp_1(5) -> 1
          y_0() -> 2
** Step 1.b:2: EmptyProcessor.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            active(f(x)) -> mark(f(f(x)))
            chk(no(c())) -> active(c())
            chk(no(f(x))) -> f(chk(mat(f(f(f(f(f(f(f(f(f(f(X())))))))))),x)))
            f(active(x)) -> active(f(x))
            f(mark(x)) -> mark(f(x))
            f(no(x)) -> no(f(x))
            mat(f(x),c()) -> no(c())
            mat(f(x),f(y())) -> f(mat(x,y()))
            tp(mark(x)) -> tp(chk(mat(f(f(f(f(f(f(f(f(f(f(X())))))))))),x)))
        - Signature:
            {active/1,chk/1,f/1,mat/2,tp/1} / {X/0,c/0,mark/1,no/1,y/0}
        - Obligation:
             runtime complexity wrt. defined symbols {active,chk,f,mat,tp} and constructors {X,c,mark,no,y}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

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