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

** Step 1.b:1: ToInnermost.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            e(g(X)) -> e(X)
            f(a()) -> f(c(a()))
            f(a()) -> f(d(a()))
            f(c(X)) -> X
            f(c(a())) -> f(d(b()))
            f(c(b())) -> f(d(a()))
            f(d(X)) -> X
        - Signature:
            {e/1,f/1} / {a/0,b/0,c/1,d/1,g/1}
        - Obligation:
             runtime complexity wrt. defined symbols {e,f} and constructors {a,b,c,d,g}
    + Applied Processor:
        ToInnermost
    + Details:
        switch to innermost, as the system is overlay and right linear and does not contain weak rules
** Step 1.b:2: Bounds.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            e(g(X)) -> e(X)
            f(a()) -> f(c(a()))
            f(a()) -> f(d(a()))
            f(c(X)) -> X
            f(c(a())) -> f(d(b()))
            f(c(b())) -> f(d(a()))
            f(d(X)) -> X
        - Signature:
            {e/1,f/1} / {a/0,b/0,c/1,d/1,g/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {e,f} and constructors {a,b,c,d,g}
    + 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() -> 1
          a_0() -> 2
          a_1() -> 1
          a_1() -> 4
          a_2() -> 1
          a_2() -> 6
          b_0() -> 1
          b_0() -> 2
          b_1() -> 1
          b_1() -> 4
          b_2() -> 1
          b_2() -> 6
          c_0(2) -> 1
          c_0(2) -> 2
          c_1(4) -> 3
          d_0(2) -> 1
          d_0(2) -> 2
          d_1(4) -> 3
          d_2(6) -> 5
          e_0(2) -> 1
          e_1(2) -> 1
          f_0(2) -> 1
          f_1(3) -> 1
          f_2(5) -> 1
          g_0(2) -> 1
          g_0(2) -> 2
          2 -> 1
          4 -> 1
          6 -> 1
** Step 1.b:3: EmptyProcessor.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            e(g(X)) -> e(X)
            f(a()) -> f(c(a()))
            f(a()) -> f(d(a()))
            f(c(X)) -> X
            f(c(a())) -> f(d(b()))
            f(c(b())) -> f(d(a()))
            f(d(X)) -> X
        - Signature:
            {e/1,f/1} / {a/0,b/0,c/1,d/1,g/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {e,f} and constructors {a,b,c,d,g}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

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