Deriv Compl Full Rewri 33144 pair #381922101

details

property	value
status	complete
benchmark	2.47.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n048.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	tct 2018-07-13
configuration	tct_dc
runtime (wallclock)	30.1176130772 seconds
cpu usage	81.762241079
max memory	6.3320064E7

stage attributes

key	value
output-size	3199
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: NaturalMI WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict TRS:
            a(b(x)) -> b(a(x))
            a(c(x)) -> x
        - 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 + [64] 
          p(b) = [1] x1 + [144]
          p(c) = [1] x1 + [148]
        
        Following rules are strictly oriented:
        a(c(x)) = [1] x + [212]
                > [1] x + [0]  
                = x            
        
        
        Following rules are (at-least) weakly oriented:
        a(b(x)) =  [1] x + [208]
                >= [1] x + [208]
                =  b(a(x))      
        
* Step 2: NaturalMI WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict TRS:
            a(b(x)) -> b(a(x))
        - Weak TRS:
            a(c(x)) -> x
        - Signature:
            {a/1} / {b/1,c/1}
        - Obligation:
             derivational complexity wrt. signature {a,b,c}
    + 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(a) = [1 4] x1 + [0]    
                 [0 1]      [1]    
          p(b) = [1 32] x1 + [132] 
                 [0  1]      [32]  
          p(c) = [1 252] x1 + [176]
                 [0   1]      [106]
        
        Following rules are strictly oriented:
        a(b(x)) = [1 36] x + [260]
                  [0  1]     [33] 
                > [1 36] x + [164]
                  [0  1]     [33] 
                = b(a(x))         
        
        
        Following rules are (at-least) weakly oriented:
        a(c(x)) =  [1 256] x + [600]
                   [0   1]     [107]
                >= [1 0] x + [0]    
                   [0 1]     [0]    
                =  x                
        
* Step 3: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            a(b(x)) -> b(a(x))
            a(c(x)) -> x
        - 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^2))

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