WORST_CASE(?,O(1))
* Step 1: Sum WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict TRS:
            activate(X) -> X
            activate(n__zeros()) -> zeros()
            tail(cons(X,XS)) -> activate(XS)
            zeros() -> cons(0(),n__zeros())
            zeros() -> n__zeros()
        - Signature:
            {activate/1,tail/1,zeros/0} / {0/0,cons/2,n__zeros/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate,tail,zeros} and constructors {0,cons,n__zeros}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: DependencyPairs WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict TRS:
            activate(X) -> X
            activate(n__zeros()) -> zeros()
            tail(cons(X,XS)) -> activate(XS)
            zeros() -> cons(0(),n__zeros())
            zeros() -> n__zeros()
        - Signature:
            {activate/1,tail/1,zeros/0} / {0/0,cons/2,n__zeros/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate,tail,zeros} and constructors {0,cons,n__zeros}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          activate#(X) -> c_1()
          activate#(n__zeros()) -> c_2(zeros#())
          tail#(cons(X,XS)) -> c_3(activate#(XS))
          zeros#() -> c_4()
          zeros#() -> c_5()
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 3: PredecessorEstimation WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            activate#(X) -> c_1()
            activate#(n__zeros()) -> c_2(zeros#())
            tail#(cons(X,XS)) -> c_3(activate#(XS))
            zeros#() -> c_4()
            zeros#() -> c_5()
        - Weak TRS:
            activate(X) -> X
            activate(n__zeros()) -> zeros()
            tail(cons(X,XS)) -> activate(XS)
            zeros() -> cons(0(),n__zeros())
            zeros() -> n__zeros()
        - Signature:
            {activate/1,tail/1,zeros/0,activate#/1,tail#/1,zeros#/0} / {0/0,cons/2,n__zeros/0,c_1/0,c_2/1,c_3/1,c_4/0
            ,c_5/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,tail#,zeros#} and constructors {0,cons
            ,n__zeros}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,4,5}
        by application of
          Pre({1,4,5}) = {2,3}.
        Here rules are labelled as follows:
          1: activate#(X) -> c_1()
          2: activate#(n__zeros()) -> c_2(zeros#())
          3: tail#(cons(X,XS)) -> c_3(activate#(XS))
          4: zeros#() -> c_4()
          5: zeros#() -> c_5()
* Step 4: PredecessorEstimation WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            activate#(n__zeros()) -> c_2(zeros#())
            tail#(cons(X,XS)) -> c_3(activate#(XS))
        - Weak DPs:
            activate#(X) -> c_1()
            zeros#() -> c_4()
            zeros#() -> c_5()
        - Weak TRS:
            activate(X) -> X
            activate(n__zeros()) -> zeros()
            tail(cons(X,XS)) -> activate(XS)
            zeros() -> cons(0(),n__zeros())
            zeros() -> n__zeros()
        - Signature:
            {activate/1,tail/1,zeros/0,activate#/1,tail#/1,zeros#/0} / {0/0,cons/2,n__zeros/0,c_1/0,c_2/1,c_3/1,c_4/0
            ,c_5/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,tail#,zeros#} and constructors {0,cons
            ,n__zeros}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1}
        by application of
          Pre({1}) = {2}.
        Here rules are labelled as follows:
          1: activate#(n__zeros()) -> c_2(zeros#())
          2: tail#(cons(X,XS)) -> c_3(activate#(XS))
          3: activate#(X) -> c_1()
          4: zeros#() -> c_4()
          5: zeros#() -> c_5()
* Step 5: PredecessorEstimation WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            tail#(cons(X,XS)) -> c_3(activate#(XS))
        - Weak DPs:
            activate#(X) -> c_1()
            activate#(n__zeros()) -> c_2(zeros#())
            zeros#() -> c_4()
            zeros#() -> c_5()
        - Weak TRS:
            activate(X) -> X
            activate(n__zeros()) -> zeros()
            tail(cons(X,XS)) -> activate(XS)
            zeros() -> cons(0(),n__zeros())
            zeros() -> n__zeros()
        - Signature:
            {activate/1,tail/1,zeros/0,activate#/1,tail#/1,zeros#/0} / {0/0,cons/2,n__zeros/0,c_1/0,c_2/1,c_3/1,c_4/0
            ,c_5/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,tail#,zeros#} and constructors {0,cons
            ,n__zeros}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1}
        by application of
          Pre({1}) = {}.
        Here rules are labelled as follows:
          1: tail#(cons(X,XS)) -> c_3(activate#(XS))
          2: activate#(X) -> c_1()
          3: activate#(n__zeros()) -> c_2(zeros#())
          4: zeros#() -> c_4()
          5: zeros#() -> c_5()
* Step 6: RemoveWeakSuffixes WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            activate#(X) -> c_1()
            activate#(n__zeros()) -> c_2(zeros#())
            tail#(cons(X,XS)) -> c_3(activate#(XS))
            zeros#() -> c_4()
            zeros#() -> c_5()
        - Weak TRS:
            activate(X) -> X
            activate(n__zeros()) -> zeros()
            tail(cons(X,XS)) -> activate(XS)
            zeros() -> cons(0(),n__zeros())
            zeros() -> n__zeros()
        - Signature:
            {activate/1,tail/1,zeros/0,activate#/1,tail#/1,zeros#/0} / {0/0,cons/2,n__zeros/0,c_1/0,c_2/1,c_3/1,c_4/0
            ,c_5/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,tail#,zeros#} and constructors {0,cons
            ,n__zeros}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:W:activate#(X) -> c_1()
             
          
          2:W:activate#(n__zeros()) -> c_2(zeros#())
             -->_1 zeros#() -> c_5():5
             -->_1 zeros#() -> c_4():4
          
          3:W:tail#(cons(X,XS)) -> c_3(activate#(XS))
             -->_1 activate#(n__zeros()) -> c_2(zeros#()):2
             -->_1 activate#(X) -> c_1():1
          
          4:W:zeros#() -> c_4()
             
          
          5:W:zeros#() -> c_5()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          3: tail#(cons(X,XS)) -> c_3(activate#(XS))
          2: activate#(n__zeros()) -> c_2(zeros#())
          4: zeros#() -> c_4()
          5: zeros#() -> c_5()
          1: activate#(X) -> c_1()
* Step 7: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            activate(X) -> X
            activate(n__zeros()) -> zeros()
            tail(cons(X,XS)) -> activate(XS)
            zeros() -> cons(0(),n__zeros())
            zeros() -> n__zeros()
        - Signature:
            {activate/1,tail/1,zeros/0,activate#/1,tail#/1,zeros#/0} / {0/0,cons/2,n__zeros/0,c_1/0,c_2/1,c_3/1,c_4/0
            ,c_5/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,tail#,zeros#} and constructors {0,cons
            ,n__zeros}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(1))