/export/starexec/sandbox/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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YES

Problem:
 double(0()) -> 0()
 double(s(x)) -> s(s(double(x)))
 half(0()) -> 0()
 half(s(0())) -> 0()
 half(s(s(x))) -> s(half(x))
 -(x,0()) -> x
 -(s(x),s(y)) -> -(x,y)
 if(0(),y,z) -> y
 if(s(x),y,z) -> z
 half(double(x)) -> x

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [if](x0, x1, x2) = x0 + x1 + 4x2 + 4,
   
   [-](x0, x1) = x0 + x1 + 1,
   
   [half](x0) = x0,
   
   [s](x0) = x0,
   
   [double](x0) = x0 + 3,
   
   [0] = 6
  orientation:
   double(0()) = 9 >= 6 = 0()
   
   double(s(x)) = x + 3 >= x + 3 = s(s(double(x)))
   
   half(0()) = 6 >= 6 = 0()
   
   half(s(0())) = 6 >= 6 = 0()
   
   half(s(s(x))) = x >= x = s(half(x))
   
   -(x,0()) = x + 7 >= x = x
   
   -(s(x),s(y)) = x + y + 1 >= x + y + 1 = -(x,y)
   
   if(0(),y,z) = y + 4z + 10 >= y = y
   
   if(s(x),y,z) = x + y + 4z + 4 >= z = z
   
   half(double(x)) = x + 3 >= x = x
  problem:
   double(s(x)) -> s(s(double(x)))
   half(0()) -> 0()
   half(s(0())) -> 0()
   half(s(s(x))) -> s(half(x))
   -(s(x),s(y)) -> -(x,y)
  Matrix Interpretation Processor: dim=3
   
   interpretation:
                  [1 0 0]     [1 0 0]     [1]
    [-](x0, x1) = [0 0 0]x0 + [1 0 0]x1 + [1]
                  [1 0 0]     [0 0 0]     [0],
    
                 [1 0 0]     [1]
    [half](x0) = [1 0 0]x0 + [1]
                 [0 0 0]     [1],
    
              [1 0 0]  
    [s](x0) = [1 0 0]x0
              [0 0 0]  ,
    
                   [1 0 0]     [1]
    [double](x0) = [1 0 0]x0 + [1]
                   [1 0 0]     [1],
    
          [0]
    [0] = [0]
          [0]
   orientation:
                   [1 0 0]    [1]    [1 0 0]    [1]                  
    double(s(x)) = [1 0 0]x + [1] >= [1 0 0]x + [1] = s(s(double(x)))
                   [1 0 0]    [1]    [0 0 0]    [0]                  
    
                [1]    [0]      
    half(0()) = [1] >= [0] = 0()
                [1]    [0]      
    
                   [1]    [0]      
    half(s(0())) = [1] >= [0] = 0()
                   [1]    [0]      
    
                    [1 0 0]    [1]    [1 0 0]    [1]             
    half(s(s(x))) = [1 0 0]x + [1] >= [1 0 0]x + [1] = s(half(x))
                    [0 0 0]    [1]    [0 0 0]    [0]             
    
                   [1 0 0]    [1 0 0]    [1]    [1 0 0]    [1 0 0]    [1]         
    -(s(x),s(y)) = [0 0 0]x + [1 0 0]y + [1] >= [0 0 0]x + [1 0 0]y + [1] = -(x,y)
                   [1 0 0]    [0 0 0]    [0]    [1 0 0]    [0 0 0]    [0]         
   problem:
    double(s(x)) -> s(s(double(x)))
    half(s(s(x))) -> s(half(x))
    -(s(x),s(y)) -> -(x,y)
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [-](x0, x1) = x0 + x1,
     
     [half](x0) = x0 + 6,
     
     [s](x0) = x0 + 2,
     
     [double](x0) = 4x0
    orientation:
     double(s(x)) = 4x + 8 >= 4x + 4 = s(s(double(x)))
     
     half(s(s(x))) = x + 10 >= x + 8 = s(half(x))
     
     -(s(x),s(y)) = x + y + 4 >= x + y = -(x,y)
    problem:
     
    Qed