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

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