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                Quantifier Elimination                 
                          in                           
            Elementary Algebra and Geometry            
                          by                           
      Partial Cylindrical Algebraic Decomposition      
                                                       
               Version B 1.69, 16 Mar 2012
                                                       
                          by                           
                       Hoon Hong                       
                  (hhong@math.ncsu.edu)                
                                                       
With contributions by: Christopher W. Brown, George E. 
Collins, Mark J. Encarnacion, Jeremy R. Johnson        
Werner Krandick, Richard Liska, Scott McCallum,        
Nicolas Robidoux, and Stanly Steinberg                 
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Enter an informal description  between '[' and ']':
qError INPUTRD: '[' was expected.
Enter an informal description  between '[' and ']':
[A CAD for Phi using the implicit EC]Enter a variable list:
(x,y)Enter the number of free variables:
2
Enter a prenex formula:
[ [x^2 + y^2 - 1 = 0 /\ x y - 1/4 < 0] \/ [(x-4)^2 + (y-1)^2 - 1 = 0 /\ (x-4) (y-1) - 1/4 < 0] ].

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Before Normalization >
prop-eqn-const

Before Normalization >
go

Before Projection (y) >
eqn-const-list (A_2,1, A_2,3)
Before Projection (y) >
go

Before Choice >
go

Before Solution >
d-fpc-stat
          propagation    trial-eval     total
true          0             36             36
false         0            213            213
total         0            249            249

Length of the projection-based formula :468

Before Solution >
go 
An equivalent quantifier-free formula:

y^2 + x^2 - 1 >= 0 /\ y^2 - 2 y + x^2 - 8 x + 16 >= 0 /\ [ [ y^2 - 2 y + x^2 - 8 x + 16 = 0 /\ 4 x y - 16 y - 4 x + 15 < 0 ] \/ [ y^2 + x^2 - 1 = 0 /\ 4 x y - 1 < 0 ] ]


=====================  The End  =======================

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0 Garbage collections, 0 Cells and 0 Arrays reclaimed, in 0 milliseconds.
404753 Cells in AVAIL, 500000 Cells in SPACE.

System time: 19 milliseconds.
System time after the initialization: 14 milliseconds.
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