Runti Compl Full Rewri 10127 pair #381903126

details

property	value
status	complete
benchmark	2.13.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n027.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	tct 2018-07-13
configuration	tct_rc
runtime (wallclock)	0.591649055481 seconds
cpu usage	2.430204401
max memory	5.4980608E7

stage attributes

key	value
output-size	6380
starexec-result	WORST_CASE(Omega(n^1),O(n^1))

output

/export/starexec/sandbox/solver/bin/starexec_run_tct_rc /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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WORST_CASE(Omega(n^1),O(n^1))
* Step 1: Sum WORST_CASE(Omega(n^1),O(n^1))
    + Considered Problem:
        - Strict TRS:
            +(x,0()) -> x
            +(x,s(y)) -> s(+(x,y))
            +(s(x),y) -> s(+(x,y))
            double(x) -> +(x,x)
            double(0()) -> 0()
            double(s(x)) -> s(s(double(x)))
        - Signature:
            {+/2,double/1} / {0/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {+,double} and constructors {0,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            +(x,0()) -> x
            +(x,s(y)) -> s(+(x,y))
            +(s(x),y) -> s(+(x,y))
            double(x) -> +(x,x)
            double(0()) -> 0()
            double(s(x)) -> s(s(double(x)))
        - Signature:
            {+/2,double/1} / {0/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {+,double} and constructors {0,s}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          +(x,y){y -> s(y)} =
            +(x,s(y)) ->^+ s(+(x,y))
              = C[+(x,y) = +(x,y){}]

** Step 1.b:1: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            +(x,0()) -> x
            +(x,s(y)) -> s(+(x,y))
            +(s(x),y) -> s(+(x,y))
            double(x) -> +(x,x)
            double(0()) -> 0()
            double(s(x)) -> s(s(double(x)))
        - Signature:
            {+/2,double/1} / {0/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {+,double} and constructors {0,s}
    + Applied Processor:
        NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just any strict-rules}
    + Details:
        We apply a matrix interpretation of kind constructor based matrix interpretation:
        The following argument positions are considered usable:
          uargs(s) = {1}
        
        Following symbols are considered usable:
          all
        TcT has computed the following interpretation:
               p(+) = [2] x1 + [1] x2 + [0]
               p(0) = [4]                  
          p(double) = [3] x1 + [3]         
               p(s) = [1] x1 + [8]         
        
        Following rules are strictly oriented:
            +(x,0()) = [2] x + [4]         
                     > [1] x + [0]         
                     = x                   
        
           +(s(x),y) = [2] x + [1] y + [16]
                     > [2] x + [1] y + [8] 
                     = s(+(x,y))           
        
           double(x) = [3] x + [3]         
                     > [3] x + [0]         
                     = +(x,x)              
        
         double(0()) = [15]                
                     > [4]                 
                     = 0()                 
        
        double(s(x)) = [3] x + [27]        
                     > [3] x + [19]        
                     = s(s(double(x)))     
        
        
        Following rules are (at-least) weakly oriented:
        +(x,s(y)) =  [2] x + [1] y + [8]
                  >= [2] x + [1] y + [8]
                  =  s(+(x,y))

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