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

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [a](x0) = x0,
   
   [b](x0) = x0 + 1
  orientation:
   b(a(a(b(x1)))) = x1 + 2 >= x1 + 2 = b(b(a(a(x1))))
   
   b(b(b(a(x1)))) = x1 + 3 >= x1 + 2 = b(b(a(a(x1))))
   
   a(b(a(a(x1)))) = x1 + 1 >= x1 + 1 = a(a(b(a(x1))))
  problem:
   b(a(a(b(x1)))) -> b(b(a(a(x1))))
   a(b(a(a(x1)))) -> a(a(b(a(x1))))
  Matrix Interpretation Processor: dim=3
   
   interpretation:
              [1 0 0]  
    [a](x0) = [1 0 0]x0
              [0 0 0]  ,
    
              [1 1 0]     [1]
    [b](x0) = [0 0 0]x0 + [0]
              [0 0 0]     [1]
   orientation:
                     [2 2 0]     [3]    [2 0 0]     [2]                 
    b(a(a(b(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = b(b(a(a(x1))))
                     [0 0 0]     [1]    [0 0 0]     [1]                 
    
                     [2 0 0]     [1]    [2 0 0]     [1]                 
    a(b(a(a(x1)))) = [2 0 0]x1 + [1] >= [2 0 0]x1 + [1] = a(a(b(a(x1))))
                     [0 0 0]     [0]    [0 0 0]     [0]                 
   problem:
    a(b(a(a(x1)))) -> a(a(b(a(x1))))
   KBO Processor:
    weight function:
     w0 = 1
     w(a) = 1
     w(b) = 0
    precedence:
     b > a
    problem:
     
    Qed