/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: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            a(a(x1)) -> b(b(b(x1)))
            b(b(x1)) -> c(c(c(x1)))
            c(c(c(c(x1)))) -> a(b(x1))
        - Signature:
            {a/1,b/1,c/1} / {}
        - Obligation:
             derivational complexity wrt. signature {a,b,c}
    + Applied Processor:
        NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = NoUArgs, urules = NoURules, selector = Just any strict-rules}
    + Details:
        We apply a matrix interpretation of kind triangular matrix interpretation:
        
        Following symbols are considered usable:
          all
        TcT has computed the following interpretation:
          p(a) = [1] x1 + [38]
          p(b) = [1] x1 + [25]
          p(c) = [1] x1 + [16]
        
        Following rules are strictly oriented:
              a(a(x1)) = [1] x1 + [76]
                       > [1] x1 + [75]
                       = b(b(b(x1)))  
        
              b(b(x1)) = [1] x1 + [50]
                       > [1] x1 + [48]
                       = c(c(c(x1)))  
        
        c(c(c(c(x1)))) = [1] x1 + [64]
                       > [1] x1 + [63]
                       = a(b(x1))     
        
        
        Following rules are (at-least) weakly oriented:
        
* Step 2: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            a(a(x1)) -> b(b(b(x1)))
            b(b(x1)) -> c(c(c(x1)))
            c(c(c(c(x1)))) -> a(b(x1))
        - Signature:
            {a/1,b/1,c/1} / {}
        - Obligation:
             derivational complexity wrt. signature {a,b,c}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))