/export/starexec/sandbox/solver/bin/starexec_run_tct_rci /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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WORST_CASE(?,O(1))
* Step 1: Sum.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict TRS:
            2nd(cons(X,X1)) -> 2nd(cons1(X,activate(X1)))
            2nd(cons1(X,cons(Y,Z))) -> Y
            activate(X) -> X
            activate(n__from(X)) -> from(X)
            from(X) -> cons(X,n__from(s(X)))
            from(X) -> n__from(X)
        - Signature:
            {2nd/1,activate/1,from/1} / {cons/2,cons1/2,n__from/1,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {2nd,activate,from} and constructors {cons,cons1,n__from
            ,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: DependencyPairs.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict TRS:
            2nd(cons(X,X1)) -> 2nd(cons1(X,activate(X1)))
            2nd(cons1(X,cons(Y,Z))) -> Y
            activate(X) -> X
            activate(n__from(X)) -> from(X)
            from(X) -> cons(X,n__from(s(X)))
            from(X) -> n__from(X)
        - Signature:
            {2nd/1,activate/1,from/1} / {cons/2,cons1/2,n__from/1,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {2nd,activate,from} and constructors {cons,cons1,n__from
            ,s}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          2nd#(cons(X,X1)) -> c_1(2nd#(cons1(X,activate(X1))),activate#(X1))
          2nd#(cons1(X,cons(Y,Z))) -> c_2()
          activate#(X) -> c_3()
          activate#(n__from(X)) -> c_4(from#(X))
          from#(X) -> c_5()
          from#(X) -> c_6()
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 3: PredecessorEstimation.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            2nd#(cons(X,X1)) -> c_1(2nd#(cons1(X,activate(X1))),activate#(X1))
            2nd#(cons1(X,cons(Y,Z))) -> c_2()
            activate#(X) -> c_3()
            activate#(n__from(X)) -> c_4(from#(X))
            from#(X) -> c_5()
            from#(X) -> c_6()
        - Weak TRS:
            2nd(cons(X,X1)) -> 2nd(cons1(X,activate(X1)))
            2nd(cons1(X,cons(Y,Z))) -> Y
            activate(X) -> X
            activate(n__from(X)) -> from(X)
            from(X) -> cons(X,n__from(s(X)))
            from(X) -> n__from(X)
        - Signature:
            {2nd/1,activate/1,from/1,2nd#/1,activate#/1,from#/1} / {cons/2,cons1/2,n__from/1,s/1,c_1/2,c_2/0,c_3/0,c_4/1
            ,c_5/0,c_6/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {2nd#,activate#,from#} and constructors {cons,cons1
            ,n__from,s}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {2,3,5,6}
        by application of
          Pre({2,3,5,6}) = {1,4}.
        Here rules are labelled as follows:
          1: 2nd#(cons(X,X1)) -> c_1(2nd#(cons1(X,activate(X1))),activate#(X1))
          2: 2nd#(cons1(X,cons(Y,Z))) -> c_2()
          3: activate#(X) -> c_3()
          4: activate#(n__from(X)) -> c_4(from#(X))
          5: from#(X) -> c_5()
          6: from#(X) -> c_6()
* Step 4: PredecessorEstimation.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            2nd#(cons(X,X1)) -> c_1(2nd#(cons1(X,activate(X1))),activate#(X1))
            activate#(n__from(X)) -> c_4(from#(X))
        - Weak DPs:
            2nd#(cons1(X,cons(Y,Z))) -> c_2()
            activate#(X) -> c_3()
            from#(X) -> c_5()
            from#(X) -> c_6()
        - Weak TRS:
            2nd(cons(X,X1)) -> 2nd(cons1(X,activate(X1)))
            2nd(cons1(X,cons(Y,Z))) -> Y
            activate(X) -> X
            activate(n__from(X)) -> from(X)
            from(X) -> cons(X,n__from(s(X)))
            from(X) -> n__from(X)
        - Signature:
            {2nd/1,activate/1,from/1,2nd#/1,activate#/1,from#/1} / {cons/2,cons1/2,n__from/1,s/1,c_1/2,c_2/0,c_3/0,c_4/1
            ,c_5/0,c_6/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {2nd#,activate#,from#} and constructors {cons,cons1
            ,n__from,s}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {2}
        by application of
          Pre({2}) = {1}.
        Here rules are labelled as follows:
          1: 2nd#(cons(X,X1)) -> c_1(2nd#(cons1(X,activate(X1))),activate#(X1))
          2: activate#(n__from(X)) -> c_4(from#(X))
          3: 2nd#(cons1(X,cons(Y,Z))) -> c_2()
          4: activate#(X) -> c_3()
          5: from#(X) -> c_5()
          6: from#(X) -> c_6()
* Step 5: PredecessorEstimation.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            2nd#(cons(X,X1)) -> c_1(2nd#(cons1(X,activate(X1))),activate#(X1))
        - Weak DPs:
            2nd#(cons1(X,cons(Y,Z))) -> c_2()
            activate#(X) -> c_3()
            activate#(n__from(X)) -> c_4(from#(X))
            from#(X) -> c_5()
            from#(X) -> c_6()
        - Weak TRS:
            2nd(cons(X,X1)) -> 2nd(cons1(X,activate(X1)))
            2nd(cons1(X,cons(Y,Z))) -> Y
            activate(X) -> X
            activate(n__from(X)) -> from(X)
            from(X) -> cons(X,n__from(s(X)))
            from(X) -> n__from(X)
        - Signature:
            {2nd/1,activate/1,from/1,2nd#/1,activate#/1,from#/1} / {cons/2,cons1/2,n__from/1,s/1,c_1/2,c_2/0,c_3/0,c_4/1
            ,c_5/0,c_6/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {2nd#,activate#,from#} and constructors {cons,cons1
            ,n__from,s}
    + 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: 2nd#(cons(X,X1)) -> c_1(2nd#(cons1(X,activate(X1))),activate#(X1))
          2: 2nd#(cons1(X,cons(Y,Z))) -> c_2()
          3: activate#(X) -> c_3()
          4: activate#(n__from(X)) -> c_4(from#(X))
          5: from#(X) -> c_5()
          6: from#(X) -> c_6()
* Step 6: RemoveWeakSuffixes.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            2nd#(cons(X,X1)) -> c_1(2nd#(cons1(X,activate(X1))),activate#(X1))
            2nd#(cons1(X,cons(Y,Z))) -> c_2()
            activate#(X) -> c_3()
            activate#(n__from(X)) -> c_4(from#(X))
            from#(X) -> c_5()
            from#(X) -> c_6()
        - Weak TRS:
            2nd(cons(X,X1)) -> 2nd(cons1(X,activate(X1)))
            2nd(cons1(X,cons(Y,Z))) -> Y
            activate(X) -> X
            activate(n__from(X)) -> from(X)
            from(X) -> cons(X,n__from(s(X)))
            from(X) -> n__from(X)
        - Signature:
            {2nd/1,activate/1,from/1,2nd#/1,activate#/1,from#/1} / {cons/2,cons1/2,n__from/1,s/1,c_1/2,c_2/0,c_3/0,c_4/1
            ,c_5/0,c_6/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {2nd#,activate#,from#} and constructors {cons,cons1
            ,n__from,s}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:W:2nd#(cons(X,X1)) -> c_1(2nd#(cons1(X,activate(X1))),activate#(X1))
             -->_2 activate#(n__from(X)) -> c_4(from#(X)):4
             -->_2 activate#(X) -> c_3():3
             -->_1 2nd#(cons1(X,cons(Y,Z))) -> c_2():2
          
          2:W:2nd#(cons1(X,cons(Y,Z))) -> c_2()
             
          
          3:W:activate#(X) -> c_3()
             
          
          4:W:activate#(n__from(X)) -> c_4(from#(X))
             -->_1 from#(X) -> c_6():6
             -->_1 from#(X) -> c_5():5
          
          5:W:from#(X) -> c_5()
             
          
          6:W:from#(X) -> c_6()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          1: 2nd#(cons(X,X1)) -> c_1(2nd#(cons1(X,activate(X1))),activate#(X1))
          2: 2nd#(cons1(X,cons(Y,Z))) -> c_2()
          3: activate#(X) -> c_3()
          4: activate#(n__from(X)) -> c_4(from#(X))
          5: from#(X) -> c_5()
          6: from#(X) -> c_6()
* Step 7: EmptyProcessor.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            2nd(cons(X,X1)) -> 2nd(cons1(X,activate(X1)))
            2nd(cons1(X,cons(Y,Z))) -> Y
            activate(X) -> X
            activate(n__from(X)) -> from(X)
            from(X) -> cons(X,n__from(s(X)))
            from(X) -> n__from(X)
        - Signature:
            {2nd/1,activate/1,from/1,2nd#/1,activate#/1,from#/1} / {cons/2,cons1/2,n__from/1,s/1,c_1/2,c_2/0,c_3/0,c_4/1
            ,c_5/0,c_6/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {2nd#,activate#,from#} and constructors {cons,cons1
            ,n__from,s}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(1))