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

** Step 1.b:1: ToInnermost.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            f(.(.(x,y),z)) -> f(.(x,.(y,z)))
            f(.(nil(),y)) -> .(nil(),f(y))
            f(nil()) -> nil()
            g(.(x,.(y,z))) -> g(.(.(x,y),z))
            g(.(x,nil())) -> .(g(x),nil())
            g(nil()) -> nil()
        - Signature:
            {f/1,g/1} / {./2,nil/0}
        - Obligation:
             runtime complexity wrt. defined symbols {f,g} and constructors {.,nil}
    + 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:
            f(.(.(x,y),z)) -> f(.(x,.(y,z)))
            f(.(nil(),y)) -> .(nil(),f(y))
            f(nil()) -> nil()
            g(.(x,.(y,z))) -> g(.(.(x,y),z))
            g(.(x,nil())) -> .(g(x),nil())
            g(nil()) -> nil()
        - Signature:
            {f/1,g/1} / {./2,nil/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,g} and constructors {.,nil}
    + Applied Processor:
        Bounds {initialAutomaton = minimal, enrichment = match}
    + Details:
        The problem is match-bounded by 1.
        The enriched problem is compatible with follwoing automaton.
          ._0(2,2) -> 2
          ._1(2,2) -> 4
          ._1(2,3) -> 3
          ._1(2,4) -> 3
          ._1(4,2) -> 7
          ._1(5,6) -> 1
          ._1(5,6) -> 5
          ._1(6,6) -> 6
          ._1(7,2) -> 7
          f_0(2) -> 1
          f_1(2) -> 6
          f_1(3) -> 1
          f_1(3) -> 6
          f_1(4) -> 6
          g_0(2) -> 1
          g_1(2) -> 5
          g_1(4) -> 5
          g_1(7) -> 1
          g_1(7) -> 5
          nil_0() -> 2
          nil_1() -> 1
          nil_1() -> 5
          nil_1() -> 6
** Step 1.b:3: EmptyProcessor.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            f(.(.(x,y),z)) -> f(.(x,.(y,z)))
            f(.(nil(),y)) -> .(nil(),f(y))
            f(nil()) -> nil()
            g(.(x,.(y,z))) -> g(.(.(x,y),z))
            g(.(x,nil())) -> .(g(x),nil())
            g(nil()) -> nil()
        - Signature:
            {f/1,g/1} / {./2,nil/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,g} and constructors {.,nil}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

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