Deriv Compl Full Rewri 33144 pair #381921994

details

property	value
status	complete
benchmark	27.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n075.star.cs.uiowa.edu
space	Der95

run statistics

property	value
solver	tct 2018-07-13
configuration	tct_dc
runtime (wallclock)	30.1186599731 seconds
cpu usage	91.146596386
max memory	4.296704E7

stage attributes

key	value
output-size	3625
starexec-result	WORST_CASE(?,O(n^2))

output

/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^2))
* Step 1: WeightGap WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict TRS:
            g(x,y) -> h(x,y)
            h(f(x),y) -> f(g(x,y))
        - Signature:
            {g/2,h/2} / {f/1}
        - Obligation:
             derivational complexity wrt. signature {f,g,h}
    + 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(f) = [1] x1 + [8]         
            p(g) = [1] x1 + [1] x2 + [0]
            p(h) = [1] x1 + [1] x2 + [5]
          
          Following rules are strictly oriented:
          h(f(x),y) = [1] x + [1] y + [13]
                    > [1] x + [1] y + [8] 
                    = f(g(x,y))           
          
          
          Following rules are (at-least) weakly oriented:
          g(x,y) =  [1] x + [1] y + [0]
                 >= [1] x + [1] y + [5]
                 =  h(x,y)             
          
        Further, it can be verified that all rules not oriented are covered by the weightgap condition.
* Step 2: NaturalMI WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict TRS:
            g(x,y) -> h(x,y)
        - Weak TRS:
            h(f(x),y) -> f(g(x,y))
        - Signature:
            {g/2,h/2} / {f/1}
        - Obligation:
             derivational complexity wrt. signature {f,g,h}
    + Applied Processor:
        NaturalMI {miDimension = 2, miDegree = 2, 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(f) = [1 0] x1 + [0]            
                 [0 1]      [2]            
          p(g) = [1 1] x1 + [1 0] x2 + [10]
                 [0 1]      [0 1]      [2] 
          p(h) = [1 1] x1 + [1 0] x2 + [8] 
                 [0 1]      [0 1]      [2] 
        
        Following rules are strictly oriented:
        g(x,y) = [1 1] x + [1 0] y + [10]
                 [0 1]     [0 1]     [2] 
               > [1 1] x + [1 0] y + [8] 
                 [0 1]     [0 1]     [2] 
               = h(x,y)                  
        
        
        Following rules are (at-least) weakly oriented:
        h(f(x),y) =  [1 1] x + [1 0] y + [10]
                     [0 1]     [0 1]     [4] 
                  >= [1 1] x + [1 0] y + [10]
                     [0 1]     [0 1]     [4] 
                  =  f(g(x,y))               
        
* Step 3: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            g(x,y) -> h(x,y)
            h(f(x),y) -> f(g(x,y))
        - Signature:
            {g/2,h/2} / {f/1}
        - Obligation:
             derivational complexity wrt. signature {f,g,h}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^2))

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