/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:
            0() -> n__0()
            activate(X) -> X
            activate(n__0()) -> 0()
            activate(n__f(X)) -> f(activate(X))
            activate(n__s(X)) -> s(activate(X))
            f(X) -> n__f(X)
            f(0()) -> cons(0(),n__f(n__s(n__0())))
            f(s(0())) -> f(p(s(0())))
            p(s(0())) -> 0()
            s(X) -> n__s(X)
        - Signature:
            {0/0,activate/1,f/1,p/1,s/1} / {cons/2,n__0/0,n__f/1,n__s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {0,activate,f,p,s} and constructors {cons,n__0,n__f,n__s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            0() -> n__0()
            activate(X) -> X
            activate(n__0()) -> 0()
            activate(n__f(X)) -> f(activate(X))
            activate(n__s(X)) -> s(activate(X))
            f(X) -> n__f(X)
            f(0()) -> cons(0(),n__f(n__s(n__0())))
            f(s(0())) -> f(p(s(0())))
            p(s(0())) -> 0()
            s(X) -> n__s(X)
        - Signature:
            {0/0,activate/1,f/1,p/1,s/1} / {cons/2,n__0/0,n__f/1,n__s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {0,activate,f,p,s} and constructors {cons,n__0,n__f,n__s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:2: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            0() -> n__0()
            activate(X) -> X
            activate(n__0()) -> 0()
            activate(n__f(X)) -> f(activate(X))
            activate(n__s(X)) -> s(activate(X))
            f(X) -> n__f(X)
            f(0()) -> cons(0(),n__f(n__s(n__0())))
            f(s(0())) -> f(p(s(0())))
            p(s(0())) -> 0()
            s(X) -> n__s(X)
        - Signature:
            {0/0,activate/1,f/1,p/1,s/1} / {cons/2,n__0/0,n__f/1,n__s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {0,activate,f,p,s} and constructors {cons,n__0,n__f,n__s}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          activate(x){x -> n__f(x)} =
            activate(n__f(x)) ->^+ f(activate(x))
              = C[activate(x) = activate(x){}]

** Step 1.b:1: Bounds.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            0() -> n__0()
            activate(X) -> X
            activate(n__0()) -> 0()
            activate(n__f(X)) -> f(activate(X))
            activate(n__s(X)) -> s(activate(X))
            f(X) -> n__f(X)
            f(0()) -> cons(0(),n__f(n__s(n__0())))
            f(s(0())) -> f(p(s(0())))
            p(s(0())) -> 0()
            s(X) -> n__s(X)
        - Signature:
            {0/0,activate/1,f/1,p/1,s/1} / {cons/2,n__0/0,n__f/1,n__s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {0,activate,f,p,s} and constructors {cons,n__0,n__f,n__s}
    + Applied Processor:
        Bounds {initialAutomaton = minimal, enrichment = match}
    + Details:
        The problem is match-bounded by 4.
        The enriched problem is compatible with follwoing automaton.
          0_0() -> 1
          0_1() -> 1
          0_1() -> 3
          0_2() -> 4
          0_3() -> 7
          activate_0(2) -> 1
          activate_1(2) -> 3
          cons_0(2,2) -> 1
          cons_0(2,2) -> 2
          cons_0(2,2) -> 3
          cons_2(4,5) -> 1
          cons_2(4,5) -> 3
          cons_3(7,9) -> 1
          cons_3(7,9) -> 3
          f_0(2) -> 1
          f_1(3) -> 1
          f_1(3) -> 3
          f_2(7) -> 1
          f_2(7) -> 3
          n__0_0() -> 1
          n__0_0() -> 2
          n__0_0() -> 3
          n__0_1() -> 1
          n__0_2() -> 1
          n__0_2() -> 3
          n__0_3() -> 4
          n__0_4() -> 7
          n__f_0(2) -> 1
          n__f_0(2) -> 2
          n__f_0(2) -> 3
          n__f_1(2) -> 1
          n__f_2(3) -> 1
          n__f_2(3) -> 3
          n__f_2(6) -> 5
          n__f_3(7) -> 1
          n__f_3(7) -> 3
          n__f_3(8) -> 9
          n__s_0(2) -> 1
          n__s_0(2) -> 2
          n__s_0(2) -> 3
          n__s_1(2) -> 1
          n__s_2(1) -> 6
          n__s_2(3) -> 1
          n__s_2(3) -> 3
          n__s_3(4) -> 8
          p_0(2) -> 1
          p_2(8) -> 7
          s_0(2) -> 1
          s_1(3) -> 1
          s_1(3) -> 3
          s_2(4) -> 8
          2 -> 1
          2 -> 3
** Step 1.b:2: EmptyProcessor.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            0() -> n__0()
            activate(X) -> X
            activate(n__0()) -> 0()
            activate(n__f(X)) -> f(activate(X))
            activate(n__s(X)) -> s(activate(X))
            f(X) -> n__f(X)
            f(0()) -> cons(0(),n__f(n__s(n__0())))
            f(s(0())) -> f(p(s(0())))
            p(s(0())) -> 0()
            s(X) -> n__s(X)
        - Signature:
            {0/0,activate/1,f/1,p/1,s/1} / {cons/2,n__0/0,n__f/1,n__s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {0,activate,f,p,s} and constructors {cons,n__0,n__f,n__s}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

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