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


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WORST_CASE(?,O(n^1))
* Step 1: NaturalMI.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            b(u(x)) -> a(e(x))
            c(u(x)) -> b(x)
            d(x) -> e(u(x))
            d(u(x)) -> c(x)
            v(e(x)) -> x
        - Signature:
            {b/1,c/1,d/1,v/1} / {a/1,e/1,u/1}
        - Obligation:
             derivational complexity wrt. signature {a,b,c,d,e,u,v}
    + 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 + [1] 
          p(b) = [1] x1 + [8] 
          p(c) = [1] x1 + [9] 
          p(d) = [1] x1 + [13]
          p(e) = [1] x1 + [5] 
          p(u) = [1] x1 + [0] 
          p(v) = [1] x1 + [6] 
        
        Following rules are strictly oriented:
        b(u(x)) = [1] x + [8] 
                > [1] x + [6] 
                = a(e(x))     
        
        c(u(x)) = [1] x + [9] 
                > [1] x + [8] 
                = b(x)        
        
           d(x) = [1] x + [13]
                > [1] x + [5] 
                = e(u(x))     
        
        d(u(x)) = [1] x + [13]
                > [1] x + [9] 
                = c(x)        
        
        v(e(x)) = [1] x + [11]
                > [1] x + [0] 
                = x           
        
        
        Following rules are (at-least) weakly oriented:
        
* Step 2: EmptyProcessor.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            b(u(x)) -> a(e(x))
            c(u(x)) -> b(x)
            d(x) -> e(u(x))
            d(u(x)) -> c(x)
            v(e(x)) -> x
        - Signature:
            {b/1,c/1,d/1,v/1} / {a/1,e/1,u/1}
        - Obligation:
             derivational complexity wrt. signature {a,b,c,d,e,u,v}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))