/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(c(c(c(x1)))) -> d(d(x1))
            b(d(x1)) -> c(c(x1))
            c(x1) -> a(a(a(a(x1))))
            c(c(c(a(x1)))) -> d(d(x1))
            d(x1) -> b(b(b(b(x1))))
            d(b(x1)) -> c(c(x1))
        - Signature:
            {a/1,b/1,c/1,d/1} / {}
        - Obligation:
             derivational complexity wrt. signature {a,b,c,d}
    + 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 + [30] 
          p(b) = [1] x1 + [50] 
          p(c) = [1] x1 + [128]
          p(d) = [1] x1 + [207]
        
        Following rules are strictly oriented:
        b(d(x1)) = [1] x1 + [257]
                 > [1] x1 + [256]
                 = c(c(x1))      
        
           c(x1) = [1] x1 + [128]
                 > [1] x1 + [120]
                 = a(a(a(a(x1))))
        
           d(x1) = [1] x1 + [207]
                 > [1] x1 + [200]
                 = b(b(b(b(x1))))
        
        d(b(x1)) = [1] x1 + [257]
                 > [1] x1 + [256]
                 = c(c(x1))      
        
        
        Following rules are (at-least) weakly oriented:
        a(c(c(c(x1)))) =  [1] x1 + [414]
                       >= [1] x1 + [414]
                       =  d(d(x1))      
        
        c(c(c(a(x1)))) =  [1] x1 + [414]
                       >= [1] x1 + [414]
                       =  d(d(x1))      
        
* Step 2: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            a(c(c(c(x1)))) -> d(d(x1))
            c(c(c(a(x1)))) -> d(d(x1))
        - Weak TRS:
            b(d(x1)) -> c(c(x1))
            c(x1) -> a(a(a(a(x1))))
            d(x1) -> b(b(b(b(x1))))
            d(b(x1)) -> c(c(x1))
        - Signature:
            {a/1,b/1,c/1,d/1} / {}
        - Obligation:
             derivational complexity wrt. signature {a,b,c,d}
    + 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 + [10]
          p(b) = [1] x1 + [16]
          p(c) = [1] x1 + [40]
          p(d) = [1] x1 + [64]
        
        Following rules are strictly oriented:
        a(c(c(c(x1)))) = [1] x1 + [130]
                       > [1] x1 + [128]
                       = d(d(x1))      
        
        c(c(c(a(x1)))) = [1] x1 + [130]
                       > [1] x1 + [128]
                       = d(d(x1))      
        
        
        Following rules are (at-least) weakly oriented:
        b(d(x1)) =  [1] x1 + [80] 
                 >= [1] x1 + [80] 
                 =  c(c(x1))      
        
           c(x1) =  [1] x1 + [40] 
                 >= [1] x1 + [40] 
                 =  a(a(a(a(x1))))
        
           d(x1) =  [1] x1 + [64] 
                 >= [1] x1 + [64] 
                 =  b(b(b(b(x1))))
        
        d(b(x1)) =  [1] x1 + [80] 
                 >= [1] x1 + [80] 
                 =  c(c(x1))      
        
* Step 3: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            a(c(c(c(x1)))) -> d(d(x1))
            b(d(x1)) -> c(c(x1))
            c(x1) -> a(a(a(a(x1))))
            c(c(c(a(x1)))) -> d(d(x1))
            d(x1) -> b(b(b(b(x1))))
            d(b(x1)) -> c(c(x1))
        - Signature:
            {a/1,b/1,c/1,d/1} / {}
        - Obligation:
             derivational complexity wrt. signature {a,b,c,d}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))