Runti Compl Full Rewri 10127 pair #381902616

details

property	value
status	complete
benchmark	logarquot.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n073.star.cs.uiowa.edu
space	Rubio_04

run statistics

property	value
solver	tct 2018-07-13
configuration	tct_rc
runtime (wallclock)	2.15676498413 seconds
cpu usage	7.896764872
max memory	9.2475392E7

stage attributes

key	value
output-size	17947
starexec-result	WORST_CASE(Omega(n^1),O(n^3))

output

/export/starexec/sandbox2/solver/bin/starexec_run_tct_rc /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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WORST_CASE(Omega(n^1),O(n^3))
* Step 1: Sum WORST_CASE(Omega(n^1),O(n^3))
    + Considered Problem:
        - Strict TRS:
            log(s(0())) -> 0()
            log(s(s(X))) -> s(log(s(quot(X,s(s(0()))))))
            min(X,0()) -> X
            min(s(X),s(Y)) -> min(X,Y)
            quot(0(),s(Y)) -> 0()
            quot(s(X),s(Y)) -> s(quot(min(X,Y),s(Y)))
        - Signature:
            {log/1,min/2,quot/2} / {0/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {log,min,quot} 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:
            log(s(0())) -> 0()
            log(s(s(X))) -> s(log(s(quot(X,s(s(0()))))))
            min(X,0()) -> X
            min(s(X),s(Y)) -> min(X,Y)
            quot(0(),s(Y)) -> 0()
            quot(s(X),s(Y)) -> s(quot(min(X,Y),s(Y)))
        - Signature:
            {log/1,min/2,quot/2} / {0/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {log,min,quot} and constructors {0,s}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          min(x,y){x -> s(x),y -> s(y)} =
            min(s(x),s(y)) ->^+ min(x,y)
              = C[min(x,y) = min(x,y){}]

** Step 1.b:1: NaturalMI WORST_CASE(?,O(n^3))
    + Considered Problem:
        - Strict TRS:
            log(s(0())) -> 0()
            log(s(s(X))) -> s(log(s(quot(X,s(s(0()))))))
            min(X,0()) -> X
            min(s(X),s(Y)) -> min(X,Y)
            quot(0(),s(Y)) -> 0()
            quot(s(X),s(Y)) -> s(quot(min(X,Y),s(Y)))
        - Signature:
            {log/1,min/2,quot/2} / {0/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {log,min,quot} 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(log) = {1},
          uargs(min) = {1},
          uargs(quot) = {1},
          uargs(s) = {1}
        
        Following symbols are considered usable:
          all
        TcT has computed the following interpretation:
             p(0) = [0]         
           p(log) = [1] x1 + [2]
           p(min) = [1] x1 + [0]
          p(quot) = [1] x1 + [0]
             p(s) = [1] x1 + [1]
        
        Following rules are strictly oriented:
           log(s(0())) = [3]        
                       > [0]        
                       = 0()        
        
        min(s(X),s(Y)) = [1] X + [1]
                       > [1] X + [0]
                       = min(X,Y)   
        
        
        Following rules are (at-least) weakly oriented:
           log(s(s(X))) =  [1] X + [4]                 
                        >= [1] X + [4]                 
                        =  s(log(s(quot(X,s(s(0()))))))
        
             min(X,0()) =  [1] X + [0]                 
                        >= [1] X + [0]                 
                        =  X                           
        
         quot(0(),s(Y)) =  [0]                         
                        >= [0]                         
                        =  0()

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