/export/starexec/sandbox/solver/bin/starexec_run_tct_rci /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:
            h(f(x,y)) -> f(f(a(),h(h(y))),x)
        - Signature:
            {h/1} / {a/0,f/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {h} and constructors {a,f}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            h(f(x,y)) -> f(f(a(),h(h(y))),x)
        - Signature:
            {h/1} / {a/0,f/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {h} and constructors {a,f}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          h(y){y -> f(x,y)} =
            h(f(x,y)) ->^+ f(f(a(),h(h(y))),x)
              = C[h(y) = h(y){}]

** Step 1.b:1: Bounds WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            h(f(x,y)) -> f(f(a(),h(h(y))),x)
        - Signature:
            {h/1} / {a/0,f/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {h} and constructors {a,f}
    + Applied Processor:
        Bounds {initialAutomaton = perSymbol, enrichment = match}
    + Details:
        The problem is match-bounded by 2.
        The enriched problem is compatible with follwoing automaton.
          a_0() -> 1
          a_1() -> 5
          a_2() -> 9
          f_0(1,1) -> 2
          f_0(1,2) -> 2
          f_0(2,1) -> 2
          f_0(2,2) -> 2
          f_1(4,1) -> 3
          f_1(4,1) -> 7
          f_1(4,1) -> 11
          f_1(4,2) -> 3
          f_1(4,2) -> 7
          f_1(4,2) -> 11
          f_1(5,6) -> 4
          f_2(8,4) -> 6
          f_2(8,4) -> 10
          f_2(9,10) -> 8
          h_0(1) -> 3
          h_0(2) -> 3
          h_1(1) -> 7
          h_1(2) -> 7
          h_1(7) -> 6
          h_2(1) -> 11
          h_2(2) -> 11
          h_2(11) -> 10
** Step 1.b:2: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            h(f(x,y)) -> f(f(a(),h(h(y))),x)
        - Signature:
            {h/1} / {a/0,f/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {h} and constructors {a,f}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

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