Deriv Compl Full Rewri 33144 pair #381922406

details

property	value
status	complete
benchmark	2.09.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n055.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	tct 2018-07-13
configuration	tct_dc
runtime (wallclock)	30.136070013 seconds
cpu usage	82.668039296
max memory	1.76959488E8

stage attributes

key	value
output-size	3799
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:
            +(0(),y) -> y
            +(s(x),y) -> +(x,s(y))
            +(s(x),y) -> s(+(x,y))
        - Signature:
            {+/2} / {0/0,s/1}
        - Obligation:
             derivational complexity wrt. signature {+,0,s}
    + 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(+) = [1] x1 + [1] x2 + [8]
          p(0) = [0]                  
          p(s) = [1] x1 + [0]         
        
        Following rules are strictly oriented:
        +(0(),y) = [1] y + [8]
                 > [1] y + [0]
                 = y          
        
        
        Following rules are (at-least) weakly oriented:
        +(s(x),y) =  [1] x + [1] y + [8]
                  >= [1] x + [1] y + [8]
                  =  +(x,s(y))          
        
        +(s(x),y) =  [1] x + [1] y + [8]
                  >= [1] x + [1] y + [8]
                  =  s(+(x,y))          
        
* Step 2: NaturalMI WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict TRS:
            +(s(x),y) -> +(x,s(y))
            +(s(x),y) -> s(+(x,y))
        - Weak TRS:
            +(0(),y) -> y
        - Signature:
            {+/2} / {0/0,s/1}
        - Obligation:
             derivational complexity wrt. signature {+,0,s}
    + 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(+) = [1 7] x1 + [1 6] x2 + [2]
                 [0 1]      [0 1]      [2]
          p(0) = [6]                      
                 [1]                      
          p(s) = [1 0] x1 + [0]           
                 [0 1]      [1]           
        
        Following rules are strictly oriented:
        +(s(x),y) = [1 7] x + [1 6] y + [9]
                    [0 1]     [0 1]     [3]
                  > [1 7] x + [1 6] y + [8]
                    [0 1]     [0 1]     [3]
                  = +(x,s(y))              
        
        +(s(x),y) = [1 7] x + [1 6] y + [9]
                    [0 1]     [0 1]     [3]
                  > [1 7] x + [1 6] y + [2]
                    [0 1]     [0 1]     [3]
                  = s(+(x,y))              
        
        
        Following rules are (at-least) weakly oriented:
        +(0(),y) =  [1 6] y + [15]
                    [0 1]     [3] 
                 >= [1 0] y + [0] 
                    [0 1]     [0] 
                 =  y             
        
* Step 3: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            +(0(),y) -> y
            +(s(x),y) -> +(x,s(y))
            +(s(x),y) -> s(+(x,y))
        - Signature:
            {+/2} / {0/0,s/1}
        - Obligation:

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