Deriv Compl Full Rewri 33144 pair #381922618

details

property	value
status	complete
benchmark	ExProp7_Luc06_FR.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n028.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	tct 2018-07-13
configuration	tct_dc
runtime (wallclock)	33.1811239719 seconds
cpu usage	114.081543121
max memory	2.00876032E8

stage attributes

key	value
output-size	31190
starexec-result	WORST_CASE(?,O(n^2))

output

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


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WORST_CASE(?,O(n^2))
* Step 1: WeightGap WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict TRS:
            0() -> n__0()
            activate(X) -> X
            activate(n__0()) -> 0()
            activate(n__f(X)) -> f(activate(X))
            activate(n__s(X)) -> s(activate(X))
            f(X) -> n__f(X)
            f(0()) -> cons(0(),n__f(n__s(n__0())))
            f(s(0())) -> f(p(s(0())))
            p(s(X)) -> X
            s(X) -> n__s(X)
        - Signature:
            {0/0,activate/1,f/1,p/1,s/1} / {cons/2,n__0/0,n__f/1,n__s/1}
        - Obligation:
             derivational complexity wrt. signature {0,activate,cons,f,n__0,n__f,n__s,p,s}
    + 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(0) = [0]                  
            p(activate) = [1] x1 + [0]         
                p(cons) = [1] x1 + [1] x2 + [0]
                   p(f) = [1] x1 + [0]         
                p(n__0) = [0]                  
                p(n__f) = [1] x1 + [0]         
                p(n__s) = [1] x1 + [0]         
                   p(p) = [1] x1 + [0]         
                   p(s) = [1] x1 + [11]        
          
          Following rules are strictly oriented:
          p(s(X)) = [1] X + [11]
                  > [1] X + [0] 
                  = X           
          
             s(X) = [1] X + [11]
                  > [1] X + [0] 
                  = n__s(X)     
          
          
          Following rules are (at-least) weakly oriented:
                        0() =  [0]                         
                            >= [0]                         
                            =  n__0()                      
          
                activate(X) =  [1] X + [0]                 
                            >= [1] X + [0]                 
                            =  X                           
          
           activate(n__0()) =  [0]                         
                            >= [0]                         
                            =  0()                         
          
          activate(n__f(X)) =  [1] X + [0]                 
                            >= [1] X + [0]                 
                            =  f(activate(X))              
          
          activate(n__s(X)) =  [1] X + [0]                 
                            >= [1] X + [11]                
                            =  s(activate(X))              
          
                       f(X) =  [1] X + [0]                 
                            >= [1] X + [0]                 
                            =  n__f(X)                     
          
                     f(0()) =  [0]                         
                            >= [0]                         
                            =  cons(0(),n__f(n__s(n__0())))
          
                  f(s(0())) =  [11]                        
                            >= [11]                        
                            =  f(p(s(0())))                
          
        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:
            0() -> n__0()
            activate(X) -> X
            activate(n__0()) -> 0()
            activate(n__f(X)) -> f(activate(X))
            activate(n__s(X)) -> s(activate(X))
            f(X) -> n__f(X)
            f(0()) -> cons(0(),n__f(n__s(n__0())))
            f(s(0())) -> f(p(s(0())))
        - Weak TRS:
            p(s(X)) -> X

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