/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:
 strict:
  a(a(b(b(x1)))) -> x1
 weak:
  b(a(x1)) -> a(b(a(b(x1))))

Proof:
 Matrix Interpretation Processor: dim=4
  
  interpretation:
             [1 1 0 0]  
             [0 0 0 1]  
   [a](x0) = [0 1 0 0]x0
             [0 0 0 1]  ,
   
             [1 0 0 0]     [0]
             [0 0 0 0]     [0]
   [b](x0) = [0 2 1 1]x0 + [1]
             [0 0 1 0]     [0]
  orientation:
                    [1 2 1 1]     [1]           
                    [0 2 1 1]     [1]           
   a(a(b(b(x1)))) = [0 2 1 1]x1 + [1] >= x1 = x1
                    [0 2 1 1]     [1]           
   
              [1 1 0 0]     [0]    [1 0 0 0]                   
              [0 0 0 0]     [0]    [0 0 0 0]                   
   b(a(x1)) = [0 1 0 3]x1 + [1] >= [0 0 0 0]x1 = a(b(a(b(x1))))
              [0 1 0 0]     [0]    [0 0 0 0]                   
  problem:
   strict:
    
   weak:
    b(a(x1)) -> a(b(a(b(x1))))
  Qed