/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(n^1))
* Step 1: Sum WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            2nd(cons(X,n__cons(Y,Z))) -> activate(Y)
            activate(X) -> X
            activate(n__cons(X1,X2)) -> cons(X1,X2)
            activate(n__from(X)) -> from(X)
            cons(X1,X2) -> n__cons(X1,X2)
            from(X) -> cons(X,n__from(s(X)))
            from(X) -> n__from(X)
        - Signature:
            {2nd/1,activate/1,cons/2,from/1} / {n__cons/2,n__from/1,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {2nd,activate,cons,from} and constructors {n__cons,n__from,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            2nd(cons(X,n__cons(Y,Z))) -> activate(Y)
            activate(X) -> X
            activate(n__cons(X1,X2)) -> cons(X1,X2)
            activate(n__from(X)) -> from(X)
            cons(X1,X2) -> n__cons(X1,X2)
            from(X) -> cons(X,n__from(s(X)))
            from(X) -> n__from(X)
        - Signature:
            {2nd/1,activate/1,cons/2,from/1} / {n__cons/2,n__from/1,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {2nd,activate,cons,from} and constructors {n__cons,n__from,s}
    + Applied Processor:
        NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just any strict-rules}
    + Details:
        We apply a matrix interpretation of kind constructor based matrix interpretation:
        The following argument positions are considered usable:
          none
        
        Following symbols are considered usable:
          all
        TcT has computed the following interpretation:
               p(2nd) = [4] x1 + [8]         
          p(activate) = [4] x1 + [6]         
              p(cons) = [4] x1 + [1] x2 + [2]
              p(from) = [4] x1 + [4]         
           p(n__cons) = [1] x1 + [1] x2 + [2]
           p(n__from) = [1] x1 + [0]         
                 p(s) = [0]                  
        
        Following rules are strictly oriented:
        2nd(cons(X,n__cons(Y,Z))) = [16] X + [4] Y + [4] Z + [24]
                                  > [4] Y + [6]                  
                                  = activate(Y)                  
        
                      activate(X) = [4] X + [6]                  
                                  > [1] X + [0]                  
                                  = X                            
        
         activate(n__cons(X1,X2)) = [4] X1 + [4] X2 + [14]       
                                  > [4] X1 + [1] X2 + [2]        
                                  = cons(X1,X2)                  
        
             activate(n__from(X)) = [4] X + [6]                  
                                  > [4] X + [4]                  
                                  = from(X)                      
        
                          from(X) = [4] X + [4]                  
                                  > [4] X + [2]                  
                                  = cons(X,n__from(s(X)))        
        
                          from(X) = [4] X + [4]                  
                                  > [1] X + [0]                  
                                  = n__from(X)                   
        
        
        Following rules are (at-least) weakly oriented:
        cons(X1,X2) =  [4] X1 + [1] X2 + [2]
                    >= [1] X1 + [1] X2 + [2]
                    =  n__cons(X1,X2)       
        
* Step 3: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            cons(X1,X2) -> n__cons(X1,X2)
        - Weak TRS:
            2nd(cons(X,n__cons(Y,Z))) -> activate(Y)
            activate(X) -> X
            activate(n__cons(X1,X2)) -> cons(X1,X2)
            activate(n__from(X)) -> from(X)
            from(X) -> cons(X,n__from(s(X)))
            from(X) -> n__from(X)
        - Signature:
            {2nd/1,activate/1,cons/2,from/1} / {n__cons/2,n__from/1,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {2nd,activate,cons,from} and constructors {n__cons,n__from,s}
    + Applied Processor:
        NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just any strict-rules}
    + Details:
        We apply a matrix interpretation of kind constructor based matrix interpretation:
        The following argument positions are considered usable:
          none
        
        Following symbols are considered usable:
          all
        TcT has computed the following interpretation:
               p(2nd) = [4] x1 + [2]         
          p(activate) = [6] x1 + [10]        
              p(cons) = [1] x1 + [4] x2 + [2]
              p(from) = [5] x1 + [10]        
           p(n__cons) = [1] x1 + [1] x2 + [0]
           p(n__from) = [1] x1 + [0]         
                 p(s) = [1] x1 + [2]         
        
        Following rules are strictly oriented:
        cons(X1,X2) = [1] X1 + [4] X2 + [2]
                    > [1] X1 + [1] X2 + [0]
                    = n__cons(X1,X2)       
        
        
        Following rules are (at-least) weakly oriented:
        2nd(cons(X,n__cons(Y,Z))) =  [4] X + [16] Y + [16] Z + [10]
                                  >= [6] Y + [10]                  
                                  =  activate(Y)                   
        
                      activate(X) =  [6] X + [10]                  
                                  >= [1] X + [0]                   
                                  =  X                             
        
         activate(n__cons(X1,X2)) =  [6] X1 + [6] X2 + [10]        
                                  >= [1] X1 + [4] X2 + [2]         
                                  =  cons(X1,X2)                   
        
             activate(n__from(X)) =  [6] X + [10]                  
                                  >= [5] X + [10]                  
                                  =  from(X)                       
        
                          from(X) =  [5] X + [10]                  
                                  >= [5] X + [10]                  
                                  =  cons(X,n__from(s(X)))         
        
                          from(X) =  [5] X + [10]                  
                                  >= [1] X + [0]                   
                                  =  n__from(X)                    
        
* Step 4: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            2nd(cons(X,n__cons(Y,Z))) -> activate(Y)
            activate(X) -> X
            activate(n__cons(X1,X2)) -> cons(X1,X2)
            activate(n__from(X)) -> from(X)
            cons(X1,X2) -> n__cons(X1,X2)
            from(X) -> cons(X,n__from(s(X)))
            from(X) -> n__from(X)
        - Signature:
            {2nd/1,activate/1,cons/2,from/1} / {n__cons/2,n__from/1,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {2nd,activate,cons,from} and constructors {n__cons,n__from,s}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))