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


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WORST_CASE(?,O(n^1))
* Step 1: WeightGap.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            first(0(),X) -> nil()
            first(s(X),cons(Y)) -> cons(Y)
            from(X) -> cons(X)
        - Signature:
            {first/2,from/1} / {0/0,cons/1,nil/0,s/1}
        - Obligation:
             derivational complexity wrt. signature {0,cons,first,from,nil,s}
    + Applied Processor:
        WeightGap {wgDimension = 1, wgDegree = 1, wgKind = Algebraic, wgUArgs = NoUArgs, wgOn = WgOnAny}
    + Details:
        The weightgap principle applies using the following nonconstant growth matrix-interpretation:
          We apply a matrix interpretation of kind triangular matrix interpretation:
          
          Following symbols are considered usable:
            all
          TcT has computed the following interpretation:
                p(0) = [0]                  
             p(cons) = [1] x1 + [0]         
            p(first) = [1] x1 + [1] x2 + [5]
             p(from) = [1] x1 + [1]         
              p(nil) = [0]                  
                p(s) = [1] x1 + [0]         
          
          Following rules are strictly oriented:
                 first(0(),X) = [1] X + [5]        
                              > [0]                
                              = nil()              
          
          first(s(X),cons(Y)) = [1] X + [1] Y + [5]
                              > [1] Y + [0]        
                              = cons(Y)            
          
                      from(X) = [1] X + [1]        
                              > [1] X + [0]        
                              = cons(X)            
          
          
          Following rules are (at-least) weakly oriented:
          
        Further, it can be verified that all rules not oriented are covered by the weightgap condition.
* Step 2: EmptyProcessor.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            first(0(),X) -> nil()
            first(s(X),cons(Y)) -> cons(Y)
            from(X) -> cons(X)
        - Signature:
            {first/2,from/1} / {0/0,cons/1,nil/0,s/1}
        - Obligation:
             derivational complexity wrt. signature {0,cons,first,from,nil,s}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))