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

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