/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


YES

Problem:
 double(0()) -> 0()
 double(s(x)) -> s(s(double(x)))
 +(x,0()) -> x
 +(x,s(y)) -> s(+(x,y))
 +(s(x),y) -> s(+(x,y))
 double(x) -> +(x,x)

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [+](x0, x1) = 2x0 + 2x1 + 4,
   
   [s](x0) = x0,
   
   [double](x0) = 4x0 + 4,
   
   [0] = 2
  orientation:
   double(0()) = 12 >= 2 = 0()
   
   double(s(x)) = 4x + 4 >= 4x + 4 = s(s(double(x)))
   
   +(x,0()) = 2x + 8 >= x = x
   
   +(x,s(y)) = 2x + 2y + 4 >= 2x + 2y + 4 = s(+(x,y))
   
   +(s(x),y) = 2x + 2y + 4 >= 2x + 2y + 4 = s(+(x,y))
   
   double(x) = 4x + 4 >= 4x + 4 = +(x,x)
  problem:
   double(s(x)) -> s(s(double(x)))
   +(x,s(y)) -> s(+(x,y))
   +(s(x),y) -> s(+(x,y))
   double(x) -> +(x,x)
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [+](x0, x1) = x0 + 2x1 + 4,
    
    [s](x0) = x0,
    
    [double](x0) = 3x0 + 5
   orientation:
    double(s(x)) = 3x + 5 >= 3x + 5 = s(s(double(x)))
    
    +(x,s(y)) = x + 2y + 4 >= x + 2y + 4 = s(+(x,y))
    
    +(s(x),y) = x + 2y + 4 >= x + 2y + 4 = s(+(x,y))
    
    double(x) = 3x + 5 >= 3x + 4 = +(x,x)
   problem:
    double(s(x)) -> s(s(double(x)))
    +(x,s(y)) -> s(+(x,y))
    +(s(x),y) -> s(+(x,y))
   Matrix Interpretation Processor: dim=3
    
    interpretation:
                   [1 0 0]     [1 1 1]  
     [+](x0, x1) = [0 1 1]x0 + [0 1 1]x1
                   [0 1 1]     [0 1 1]  ,
     
               [1 0 0]     [0]
     [s](x0) = [0 0 1]x0 + [1]
               [0 1 0]     [0],
     
                    [1 1 1]  
     [double](x0) = [0 1 1]x0
                    [0 1 1]  
    orientation:
                    [1 1 1]    [1]    [1 1 1]    [0]                  
     double(s(x)) = [0 1 1]x + [1] >= [0 1 1]x + [1] = s(s(double(x)))
                    [0 1 1]    [1]    [0 1 1]    [1]                  
     
                 [1 0 0]    [1 1 1]    [1]    [1 0 0]    [1 1 1]    [0]            
     +(x,s(y)) = [0 1 1]x + [0 1 1]y + [1] >= [0 1 1]x + [0 1 1]y + [1] = s(+(x,y))
                 [0 1 1]    [0 1 1]    [1]    [0 1 1]    [0 1 1]    [0]            
     
                 [1 0 0]    [1 1 1]    [0]    [1 0 0]    [1 1 1]    [0]            
     +(s(x),y) = [0 1 1]x + [0 1 1]y + [1] >= [0 1 1]x + [0 1 1]y + [1] = s(+(x,y))
                 [0 1 1]    [0 1 1]    [1]    [0 1 1]    [0 1 1]    [0]            
    problem:
     +(s(x),y) -> s(+(x,y))
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [+](x0, x1) = 2x0 + 4x1 + 5,
      
      [s](x0) = x0 + 1
     orientation:
      +(s(x),y) = 2x + 4y + 7 >= 2x + 4y + 6 = s(+(x,y))
     problem:
      
     Qed