/export/starexec/sandbox2/solver/bin/starexec_run_ttt2 /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

Problem:
 a(x,y) -> b(x,b(0(),c(y)))
 c(b(y,c(x))) -> c(c(b(a(0(),0()),y)))
 b(y,0()) -> y

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