/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:
 +(0(),y) -> y
 +(s(x),y) -> s(+(x,y))
 -(0(),y) -> 0()
 -(x,0()) -> x
 -(s(x),s(y)) -> -(x,y)

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