/export/starexec/sandbox/solver/bin/starexec_run_tct_rc /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:
            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:
             runtime complexity wrt. defined symbols {activate,tail,zeros} and constructors {0,cons,n__zeros}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: ToInnermost.  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:
             runtime complexity wrt. defined symbols {activate,tail,zeros} and constructors {0,cons,n__zeros}
    + Applied Processor:
        ToInnermost
    + Details:
        switch to innermost, as the system is overlay and right linear and does not contain weak rules
* Step 3: 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 4: UsableRules.  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:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          activate#(X) -> c_1()
          activate#(n__zeros()) -> c_2(zeros#())
          tail#(cons(X,XS)) -> c_3(activate#(XS))
          zeros#() -> c_4()
          zeros#() -> c_5()
* Step 5: Trivial.  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()
        - 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:
        Trivial
    + Details:
        Consider the dependency graph
          1:S:activate#(X) -> c_1()
             
          
          2:S:activate#(n__zeros()) -> c_2(zeros#())
             -->_1 zeros#() -> c_5():5
             -->_1 zeros#() -> c_4():4
          
          3:S:tail#(cons(X,XS)) -> c_3(activate#(XS))
             -->_1 activate#(n__zeros()) -> c_2(zeros#()):2
             -->_1 activate#(X) -> c_1():1
          
          4:S:zeros#() -> c_4()
             
          
          5:S:zeros#() -> c_5()
             
          
        The dependency graph contains no loops, we remove all dependency pairs.
* Step 6: EmptyProcessor.  WORST_CASE(?,O(1))
    + Considered Problem:
        
        - 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))