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


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YES

Problem:
 strict:
  f(b(x),y) -> f(x,b(y))
  f(x,a(y)) -> f(a(x),y)
 weak:
  f(x,y) -> f(a(x),y)
  f(x,y) -> f(x,b(y))

Proof:
 Matrix Interpretation Processor: dim=2
  
  interpretation:
             [1 0]  
   [a](x0) = [0 0]x0,
   
                 [2 1]     [1 0]  
   [f](x0, x1) = [0 0]x0 + [0 0]x1,
   
                  [0]
   [b](x0) = x0 + [2]
  orientation:
               [2 1]    [1 0]    [2]    [2 1]    [1 0]             
   f(b(x),y) = [0 0]x + [0 0]y + [0] >= [0 0]x + [0 0]y = f(x,b(y))
   
               [2 1]    [1 0]     [2 0]    [1 0]             
   f(x,a(y)) = [0 0]x + [0 0]y >= [0 0]x + [0 0]y = f(a(x),y)
   
            [2 1]    [1 0]     [2 0]    [1 0]             
   f(x,y) = [0 0]x + [0 0]y >= [0 0]x + [0 0]y = f(a(x),y)
   
            [2 1]    [1 0]     [2 1]    [1 0]             
   f(x,y) = [0 0]x + [0 0]y >= [0 0]x + [0 0]y = f(x,b(y))
  problem:
   strict:
    f(x,a(y)) -> f(a(x),y)
   weak:
    f(x,y) -> f(a(x),y)
    f(x,y) -> f(x,b(y))
  Matrix Interpretation Processor: dim=2
   
   interpretation:
                   [0]
    [a](x0) = x0 + [2],
    
                  [2 0]     [2 1]     [1]
    [f](x0, x1) = [0 0]x0 + [0 0]x1 + [0],
    
                
    [b](x0) = x0
   orientation:
                [2 0]    [2 1]    [3]    [2 0]    [2 1]    [1]            
    f(x,a(y)) = [0 0]x + [0 0]y + [0] >= [0 0]x + [0 0]y + [0] = f(a(x),y)
    
             [2 0]    [2 1]    [1]    [2 0]    [2 1]    [1]            
    f(x,y) = [0 0]x + [0 0]y + [0] >= [0 0]x + [0 0]y + [0] = f(a(x),y)
    
             [2 0]    [2 1]    [1]    [2 0]    [2 1]    [1]            
    f(x,y) = [0 0]x + [0 0]y + [0] >= [0 0]x + [0 0]y + [0] = f(x,b(y))
   problem:
    strict:
     
    weak:
     f(x,y) -> f(a(x),y)
     f(x,y) -> f(x,b(y))
   Qed