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

Proof:
 DP Processor:
  DPs:
   a#(a(a(x1))) -> b#(x1)
   a#(a(a(x1))) -> a#(b(x1))
   a#(a(a(x1))) -> a#(a(b(x1)))
   b#(a(b(x1))) -> a#(x1)
   b#(a(b(x1))) -> b#(a(x1))
   b#(a(b(x1))) -> a#(b(a(x1)))
  TRS:
   a(a(a(x1))) -> a(a(b(x1)))
   b(a(b(x1))) -> a(b(a(x1)))
  TDG Processor:
   DPs:
    a#(a(a(x1))) -> b#(x1)
    a#(a(a(x1))) -> a#(b(x1))
    a#(a(a(x1))) -> a#(a(b(x1)))
    b#(a(b(x1))) -> a#(x1)
    b#(a(b(x1))) -> b#(a(x1))
    b#(a(b(x1))) -> a#(b(a(x1)))
   TRS:
    a(a(a(x1))) -> a(a(b(x1)))
    b(a(b(x1))) -> a(b(a(x1)))
   graph:
    b#(a(b(x1))) -> b#(a(x1)) -> b#(a(b(x1))) -> a#(b(a(x1)))
    b#(a(b(x1))) -> b#(a(x1)) -> b#(a(b(x1))) -> b#(a(x1))
    b#(a(b(x1))) -> b#(a(x1)) -> b#(a(b(x1))) -> a#(x1)
    b#(a(b(x1))) -> a#(b(a(x1))) -> a#(a(a(x1))) -> a#(a(b(x1)))
    b#(a(b(x1))) -> a#(b(a(x1))) -> a#(a(a(x1))) -> a#(b(x1))
    b#(a(b(x1))) -> a#(b(a(x1))) -> a#(a(a(x1))) -> b#(x1)
    b#(a(b(x1))) -> a#(x1) -> a#(a(a(x1))) -> a#(a(b(x1)))
    b#(a(b(x1))) -> a#(x1) -> a#(a(a(x1))) -> a#(b(x1))
    b#(a(b(x1))) -> a#(x1) -> a#(a(a(x1))) -> b#(x1)
    a#(a(a(x1))) -> b#(x1) -> b#(a(b(x1))) -> a#(b(a(x1)))
    a#(a(a(x1))) -> b#(x1) -> b#(a(b(x1))) -> b#(a(x1))
    a#(a(a(x1))) -> b#(x1) -> b#(a(b(x1))) -> a#(x1)
    a#(a(a(x1))) -> a#(b(x1)) -> a#(a(a(x1))) -> a#(a(b(x1)))
    a#(a(a(x1))) -> a#(b(x1)) -> a#(a(a(x1))) -> a#(b(x1))
    a#(a(a(x1))) -> a#(b(x1)) -> a#(a(a(x1))) -> b#(x1)
    a#(a(a(x1))) -> a#(a(b(x1))) -> a#(a(a(x1))) -> a#(a(b(x1)))
    a#(a(a(x1))) -> a#(a(b(x1))) -> a#(a(a(x1))) -> a#(b(x1))
    a#(a(a(x1))) -> a#(a(b(x1))) -> a#(a(a(x1))) -> b#(x1)
   Arctic Interpretation Processor:
    dimension: 1
    usable rules:
     a(a(a(x1))) -> a(a(b(x1)))
     b(a(b(x1))) -> a(b(a(x1)))
    interpretation:
     [b#](x0) = 1x0 + 0,
     
     [a#](x0) = x0 + 0,
     
     [b](x0) = 2x0 + 15,
     
     [a](x0) = 2x0 + 15
    orientation:
     a#(a(a(x1))) = 4x1 + 17 >= 1x1 + 0 = b#(x1)
     
     a#(a(a(x1))) = 4x1 + 17 >= 2x1 + 15 = a#(b(x1))
     
     a#(a(a(x1))) = 4x1 + 17 >= 4x1 + 17 = a#(a(b(x1)))
     
     b#(a(b(x1))) = 5x1 + 18 >= x1 + 0 = a#(x1)
     
     b#(a(b(x1))) = 5x1 + 18 >= 3x1 + 16 = b#(a(x1))
     
     b#(a(b(x1))) = 5x1 + 18 >= 4x1 + 17 = a#(b(a(x1)))
     
     a(a(a(x1))) = 6x1 + 19 >= 6x1 + 19 = a(a(b(x1)))
     
     b(a(b(x1))) = 6x1 + 19 >= 6x1 + 19 = a(b(a(x1)))
    problem:
     DPs:
      a#(a(a(x1))) -> a#(a(b(x1)))
     TRS:
      a(a(a(x1))) -> a(a(b(x1)))
      b(a(b(x1))) -> a(b(a(x1)))
    Restore Modifier:
     DPs:
      a#(a(a(x1))) -> a#(a(b(x1)))
     TRS:
      a(a(a(x1))) -> a(a(b(x1)))
      b(a(b(x1))) -> a(b(a(x1)))
     EDG Processor:
      DPs:
       a#(a(a(x1))) -> a#(a(b(x1)))
      TRS:
       a(a(a(x1))) -> a(a(b(x1)))
       b(a(b(x1))) -> a(b(a(x1)))
      graph:
       a#(a(a(x1))) -> a#(a(b(x1))) -> a#(a(a(x1))) -> a#(a(b(x1)))
      Arctic Interpretation Processor:
       dimension: 3
       usable rules:
        a(a(a(x1))) -> a(a(b(x1)))
        b(a(b(x1))) -> a(b(a(x1)))
       interpretation:
        [a#](x0) = [1 0 0]x0 + [0],
        
                  [-& 0  -&]     [0]
        [b](x0) = [-& 0  -&]x0 + [0]
                  [-& 1  1 ]     [1],
        
                  [1  1  -&]     [1 ]
        [a](x0) = [-& -& 0 ]x0 + [0 ]
                  [-& -& -&]     [-&]
       orientation:
        a#(a(a(x1))) = [3 3 2]x1 + [3] >= [-& 2  1 ]x1 + [2] = a#(a(b(x1)))
        
                      [3  3  2 ]     [3 ]    [-& 2  2 ]     [2 ]              
        a(a(a(x1))) = [-& -& -&]x1 + [0 ] >= [-& -& -&]x1 + [0 ] = a(a(b(x1)))
                      [-& -& -&]     [-&]    [-& -& -&]     [-&]              
        
                      [-& 1  1 ]     [1]    [-& -& 1 ]     [1 ]              
        b(a(b(x1))) = [-& 1  1 ]x1 + [1] >= [-& -& 1 ]x1 + [1 ] = a(b(a(x1)))
                      [-& 2  2 ]     [2]    [-& -& -&]     [-&]              
       problem:
        DPs:
         
        TRS:
         a(a(a(x1))) -> a(a(b(x1)))
         b(a(b(x1))) -> a(b(a(x1)))
       Qed