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

** Step 1.b:1: ToInnermost WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            f(+(x,y)) -> *(f(x),f(y))
            f(+(x,s(0()))) -> +(s(s(0())),f(x))
            f(0()) -> s(0())
            f(s(0())) -> *(s(s(0())),f(0()))
            f(s(0())) -> s(s(0()))
        - Signature:
            {f/1} / {*/2,+/2,0/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {f} and constructors {*,+,0,s}
    + 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)) -> *(f(x),f(y))
            f(+(x,s(0()))) -> +(s(s(0())),f(x))
            f(0()) -> s(0())
            f(s(0())) -> *(s(s(0())),f(0()))
            f(s(0())) -> s(s(0()))
        - Signature:
            {f/1} / {*/2,+/2,0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f} and constructors {*,+,0,s}
    + Applied Processor:
        Bounds {initialAutomaton = minimal, enrichment = match}
    + Details:
        The problem is match-bounded by 2.
        The enriched problem is compatible with follwoing automaton.
          *_0(2,2) -> 2
          *_1(3,4) -> 1
          *_1(4,4) -> 3
          *_1(4,4) -> 4
          *_1(5,8) -> 1
          *_1(5,8) -> 3
          *_1(5,8) -> 4
          +_0(2,2) -> 2
          +_1(5,4) -> 1
          +_1(5,4) -> 3
          +_1(5,4) -> 4
          0_0() -> 2
          0_1() -> 7
          0_2() -> 9
          f_0(2) -> 1
          f_1(2) -> 3
          f_1(2) -> 4
          f_1(7) -> 8
          s_0(2) -> 2
          s_1(6) -> 1
          s_1(6) -> 3
          s_1(6) -> 4
          s_1(6) -> 5
          s_1(7) -> 1
          s_1(7) -> 3
          s_1(7) -> 4
          s_1(7) -> 6
          s_2(9) -> 8
** Step 1.b:3: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            f(+(x,y)) -> *(f(x),f(y))
            f(+(x,s(0()))) -> +(s(s(0())),f(x))
            f(0()) -> s(0())
            f(s(0())) -> *(s(s(0())),f(0()))
            f(s(0())) -> s(s(0()))
        - Signature:
            {f/1} / {*/2,+/2,0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f} and constructors {*,+,0,s}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

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