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


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YES

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

Proof:
 String Reversal Processor:
  b(a(a(a(x1)))) -> a(a(a(b(a(b(x1))))))
  b(a(x1)) -> x1
  DP Processor:
   DPs:
    b#(a(a(a(x1)))) -> b#(x1)
    b#(a(a(a(x1)))) -> b#(a(b(x1)))
   TRS:
    b(a(a(a(x1)))) -> a(a(a(b(a(b(x1))))))
    b(a(x1)) -> x1
   Arctic Interpretation Processor:
    dimension: 3
    usable rules:
     b(a(a(a(x1)))) -> a(a(a(b(a(b(x1))))))
     b(a(x1)) -> x1
    interpretation:
     [b#](x0) = [0  -& 0 ]x0 + [0],
     
               [-& -& 0 ]     [1]
     [a](x0) = [1  -& 0 ]x0 + [0]
               [0  0  -&]     [1],
     
               [-& -& 0 ]     [1 ]
     [b](x0) = [-& -& 0 ]x0 + [0 ]
               [0  0  1 ]     [-&]
    orientation:
     b#(a(a(a(x1)))) = [1 0 1]x1 + [2] >= [0  -& 0 ]x1 + [0] = b#(x1)
     
     b#(a(a(a(x1)))) = [1 0 1]x1 + [2] >= [0 0 1]x1 + [1] = b#(a(b(x1)))
     
                      [0 0 1]     [2]    [0 0 1]     [2]                       
     b(a(a(a(x1)))) = [0 0 1]x1 + [2] >= [0 0 1]x1 + [2] = a(a(a(b(a(b(x1))))))
                      [1 1 2]     [3]    [1 1 2]     [3]                       
     
                [0  0  -&]     [1]           
     b(a(x1)) = [0  0  -&]x1 + [1] >= x1 = x1
                [1  1  0 ]     [2]           
    problem:
     DPs:
      b#(a(a(a(x1)))) -> b#(a(b(x1)))
     TRS:
      b(a(a(a(x1)))) -> a(a(a(b(a(b(x1))))))
      b(a(x1)) -> x1
    Restore Modifier:
     DPs:
      b#(a(a(a(x1)))) -> b#(a(b(x1)))
     TRS:
      b(a(a(a(x1)))) -> a(a(a(b(a(b(x1))))))
      b(a(x1)) -> x1
     Arctic Interpretation Processor:
      dimension: 3
      usable rules:
       b(a(a(a(x1)))) -> a(a(a(b(a(b(x1))))))
       b(a(x1)) -> x1
      interpretation:
       [b#](x0) = [0  -& -&]x0,
       
                 [0  -& 0 ]     [-&]
       [a](x0) = [1  0  0 ]x0 + [0 ]
                 [0  0  0 ]     [0 ],
       
                 [0  -& -&]     [-&]
       [b](x0) = [1  0  0 ]x0 + [0 ]
                 [0  -& -&]     [-&]
      orientation:
       b#(a(a(a(x1)))) = [1 0 0]x1 + [0] >= [0  -& -&]x1 = b#(a(b(x1)))
       
                        [1 0 0]     [0]    [1 0 0]     [0]                       
       b(a(a(a(x1)))) = [2 1 1]x1 + [1] >= [2 1 1]x1 + [1] = a(a(a(b(a(b(x1))))))
                        [1 0 0]     [0]    [1 0 0]     [0]                       
       
                  [0  -& 0 ]     [-&]           
       b(a(x1)) = [1  0  1 ]x1 + [0 ] >= x1 = x1
                  [0  -& 0 ]     [-&]           
      problem:
       DPs:
        
       TRS:
        b(a(a(a(x1)))) -> a(a(a(b(a(b(x1))))))
        b(a(x1)) -> x1
      Qed