/export/starexec/sandbox2/solver/bin/starexec_run_tct_rci /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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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 1.a:1: Sum.  MAYBE
    + 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 1.a:2: Ara.  MAYBE
    + 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:
        Ara {minDegree = 1, maxDegree = 3, araTimeout = 15, araRuleShifting = Just 1, isBestCase = True, mkCompletelyDefined = False, verboseOutput = False}
    + Details:
        Signatures used:
        ----------------
          F (TrsFun "0") :: [] -(0)-> "A"(0, 0, 0)
          F (TrsFun "activate") :: ["A"(0, 0, 1)] -(1)-> "A"(0, 0, 1)
          F (TrsFun "cons") :: ["A"(0, 0, 0) x "A"(0, 0, 0)] -(0)-> "A"(0, 0, 0)
          F (TrsFun "main") :: [] -(1)-> "A"(0, 0, 0)
          F (TrsFun "n__zeros") :: [] -(0)-> "A"(0, 0, 1)
          F (TrsFun "n__zeros") :: [] -(0)-> "A"(0, 0, 0)
          F (TrsFun "tail") :: ["A"(0, 0, 0)] -(1)-> "A"(0, 0, 1)
          F (TrsFun "zeros") :: [] -(0)-> "A"(0, 0, 0)
        
        
        Cost-free Signatures used:
        --------------------------
        
        
        
        Base Constructor Signatures used:
        ---------------------------------
        
        
        
        Following Still Strict Rules were Typed as:
        -------------------------------------------
        1. Strict:
          activate(X) -> X
          activate(n__zeros()) -> zeros()
          tail(cons(X,XS)) -> activate(XS)
          main() -> zeros()
        2. Weak:
          zeros() -> cons(0(),n__zeros())
          zeros() -> n__zeros()
        
** Step 1.a:3: Ara.  MAYBE
    + Considered Problem:
        - Strict TRS:
            zeros() -> cons(0(),n__zeros())
            zeros() -> n__zeros()
        - Weak TRS:
            activate(X) -> X
            activate(n__zeros()) -> zeros()
            tail(cons(X,XS)) -> activate(XS)
        - 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:
        Ara {minDegree = 1, maxDegree = 3, araTimeout = 15, araRuleShifting = Just 1, isBestCase = True, mkCompletelyDefined = False, verboseOutput = False}
    + Details:
        Signatures used:
        ----------------
          F (TrsFun "0") :: [] -(0)-> "A"(0, 0, 0)
          F (TrsFun "activate") :: ["A"(0, 0, 1)] -(0)-> "A"(0, 0, 1)
          F (TrsFun "cons") :: ["A"(0, 0, 0) x "A"(0, 0, 0)] -(0)-> "A"(0, 0, 0)
          F (TrsFun "main") :: [] -(1)-> "A"(0, 0, 0)
          F (TrsFun "n__zeros") :: [] -(0)-> "A"(0, 0, 1)
          F (TrsFun "n__zeros") :: [] -(0)-> "A"(0, 0, 0)
          F (TrsFun "tail") :: ["A"(0, 0, 0)] -(0)-> "A"(0, 0, 1)
          F (TrsFun "zeros") :: [] -(1)-> "A"(0, 0, 0)
        
        
        Cost-free Signatures used:
        --------------------------
        
        
        
        Base Constructor Signatures used:
        ---------------------------------
        
        
        
        Following Still Strict Rules were Typed as:
        -------------------------------------------
        1. Strict:
          zeros() -> cons(0(),n__zeros())
          zeros() -> n__zeros()
          main() -> zeros()
        2. Weak:
          
        

** Step 1.b:1: 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 1.b:2: 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 1.b:3: 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 1.b:4: 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 1.b:5: 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 1.b:6: 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))