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


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YES

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

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [a](x0) = x0,
   
   [b](x0) = 2x0 + 3
  orientation:
   b(a(b(b(x1)))) = 8x1 + 21 >= 4x1 + 9 = a(b(a(b(x1))))
   
   b(b(a(a(x1)))) = 4x1 + 9 >= 4x1 + 9 = a(b(a(b(x1))))
   
   b(a(a(b(x1)))) = 4x1 + 9 >= 4x1 + 9 = b(a(b(a(x1))))
  problem:
   b(b(a(a(x1)))) -> a(b(a(b(x1))))
   b(a(a(b(x1)))) -> b(a(b(a(x1))))
  Matrix Interpretation Processor: dim=3
   
   interpretation:
              [1 0 0]     [0]
    [a](x0) = [0 0 0]x0 + [0]
              [0 1 1]     [1],
    
              [1 1 0]  
    [b](x0) = [0 0 1]x0
              [0 1 0]  
   orientation:
                     [1 1 1]     [2]    [1 1 0]     [0]                 
    b(b(a(a(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = a(b(a(b(x1))))
                     [0 1 1]     [2]    [0 1 1]     [2]                 
    
                     [1 1 0]     [0]    [1 0 0]     [0]                 
    b(a(a(b(x1)))) = [0 1 1]x1 + [2] >= [0 1 1]x1 + [2] = b(a(b(a(x1))))
                     [0 0 0]     [0]    [0 0 0]     [0]                 
   problem:
    b(a(a(b(x1)))) -> b(a(b(a(x1))))
   KBO Processor:
    weight function:
     w0 = 1
     w(b) = 1
     w(a) = 0
    precedence:
     a > b
    problem:
     
    Qed