/export/starexec/sandbox/solver/bin/starexec_run_ttt2 /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=3
  
  interpretation:
                 [1 0 0]     [1 0 0]  
   [-](x0, x1) = [0 1 1]x0 + [0 0 0]x1
                 [0 1 1]     [0 0 0]  ,
   
                  [1 1 1]     [0]
   [double](x0) = [0 0 0]x0 + [1]
                  [1 0 0]     [0],
   
                [1 0 0]     [0]
   [half](x0) = [1 0 0]x0 + [1]
                [1 0 0]     [1],
   
                      [1 0 0]            
   [if](x0, x1, x2) = [0 0 0]x0 + x1 + x2
                      [0 0 1]            ,
   
         [0]
   [0] = [1]
         [0],
   
             [1 0 0]  
   [s](x0) = [0 0 1]x0
             [0 1 0]  
  orientation:
                 [1]    [0]      
   double(0()) = [1] >= [1] = 0()
                 [0]    [0]      
   
                  [1 1 1]    [0]    [1 1 1]    [0]                  
   double(s(x)) = [0 0 0]x + [1] >= [0 0 0]x + [1] = s(s(double(x)))
                  [1 0 0]    [0]    [1 0 0]    [0]                  
   
               [0]    [0]      
   half(0()) = [1] >= [1] = 0()
               [1]    [0]      
   
                  [0]    [0]      
   half(s(0())) = [1] >= [1] = 0()
                  [1]    [0]      
   
                   [1 0 0]    [0]    [1 0 0]    [0]             
   half(s(s(x))) = [1 0 0]x + [1] >= [1 0 0]x + [1] = s(half(x))
                   [1 0 0]    [1]    [1 0 0]    [1]             
   
              [1 0 0]          
   -(x,0()) = [0 1 1]x >= x = x
              [0 1 1]          
   
                  [1 0 0]    [1 0 0]     [1 0 0]    [1 0 0]          
   -(s(x),s(y)) = [0 1 1]x + [0 0 0]y >= [0 1 1]x + [0 0 0]y = -(x,y)
                  [0 1 1]    [0 0 0]     [0 1 1]    [0 0 0]          
   
                               
   if(0(),y,z) = y + z >= y = y
                               
   
                  [1 0 0]                  
   if(s(x),y,z) = [0 0 0]x + y + z >= z = z
                  [0 1 0]                  
   
                     [1 1 1]    [0]         
   half(double(x)) = [1 1 1]x + [1] >= x = x
                     [1 1 1]    [1]         
  problem:
   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
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [-](x0, x1) = x0 + 2x1 + 4,
    
    [double](x0) = x0,
    
    [half](x0) = 4x0,
    
    [if](x0, x1, x2) = 4x0 + x1 + x2,
    
    [0] = 1,
    
    [s](x0) = x0
   orientation:
    double(s(x)) = x >= x = s(s(double(x)))
    
    half(0()) = 4 >= 1 = 0()
    
    half(s(0())) = 4 >= 1 = 0()
    
    half(s(s(x))) = 4x >= 4x = s(half(x))
    
    -(x,0()) = x + 6 >= x = x
    
    -(s(x),s(y)) = x + 2y + 4 >= x + 2y + 4 = -(x,y)
    
    if(0(),y,z) = y + z + 4 >= y = y
    
    if(s(x),y,z) = 4x + y + z >= z = z
    
    half(double(x)) = 4x >= x = x
   problem:
    double(s(x)) -> s(s(double(x)))
    half(s(s(x))) -> s(half(x))
    -(s(x),s(y)) -> -(x,y)
    if(s(x),y,z) -> z
    half(double(x)) -> x
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [-](x0, x1) = x0 + x1 + 4,
     
     [double](x0) = 4x0 + 2,
     
     [half](x0) = x0 + 4,
     
     [if](x0, x1, x2) = 6x0 + 4x1 + 4x2,
     
     [s](x0) = x0 + 4
    orientation:
     double(s(x)) = 4x + 18 >= 4x + 10 = s(s(double(x)))
     
     half(s(s(x))) = x + 12 >= x + 8 = s(half(x))
     
     -(s(x),s(y)) = x + y + 12 >= x + y + 4 = -(x,y)
     
     if(s(x),y,z) = 6x + 4y + 4z + 24 >= z = z
     
     half(double(x)) = 4x + 6 >= x = x
    problem:
     
    Qed