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

** Step 1.b:1: Bounds.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            ++(x,nil()) -> x
            ++(++(x,y),z) -> ++(x,++(y,z))
            ++(nil(),y) -> y
            flatten(++(x,y)) -> ++(flatten(x),flatten(y))
            flatten(++(unit(x),y)) -> ++(flatten(x),flatten(y))
            flatten(flatten(x)) -> flatten(x)
            flatten(nil()) -> nil()
            flatten(unit(x)) -> flatten(x)
            rev(++(x,y)) -> ++(rev(y),rev(x))
            rev(nil()) -> nil()
            rev(rev(x)) -> x
            rev(unit(x)) -> unit(x)
        - Signature:
            {++/2,flatten/1,rev/1} / {nil/0,unit/1}
        - Obligation:
             runtime complexity wrt. defined symbols {++,flatten,rev} and constructors {nil,unit}
    + 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) -> 1
          flatten_0(2) -> 1
          flatten_1(2) -> 1
          nil_0() -> 1
          nil_0() -> 2
          nil_1() -> 1
          rev_0(2) -> 1
          unit_0(2) -> 1
          unit_0(2) -> 2
          unit_1(2) -> 1
          2 -> 1
** Step 1.b:2: EmptyProcessor.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            ++(x,nil()) -> x
            ++(++(x,y),z) -> ++(x,++(y,z))
            ++(nil(),y) -> y
            flatten(++(x,y)) -> ++(flatten(x),flatten(y))
            flatten(++(unit(x),y)) -> ++(flatten(x),flatten(y))
            flatten(flatten(x)) -> flatten(x)
            flatten(nil()) -> nil()
            flatten(unit(x)) -> flatten(x)
            rev(++(x,y)) -> ++(rev(y),rev(x))
            rev(nil()) -> nil()
            rev(rev(x)) -> x
            rev(unit(x)) -> unit(x)
        - Signature:
            {++/2,flatten/1,rev/1} / {nil/0,unit/1}
        - Obligation:
             runtime complexity wrt. defined symbols {++,flatten,rev} and constructors {nil,unit}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

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