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


--------------------------------------------------------------------------------


YES

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

Proof:
 DP Processor:
  DPs:
   a#(a(a(x1))) -> b#(x1)
   a#(a(a(x1))) -> b#(b(x1))
   a#(a(a(x1))) -> b#(b(b(x1)))
   a#(a(a(x1))) -> a#(b(b(b(x1))))
   b#(b(a(b(x1)))) -> a#(x1)
   b#(b(a(b(x1)))) -> a#(a(x1))
   b#(b(a(b(x1)))) -> a#(a(a(x1)))
  TRS:
   a(a(a(x1))) -> a(b(b(b(x1))))
   b(b(a(b(x1)))) -> a(a(a(x1)))
  TDG Processor:
   DPs:
    a#(a(a(x1))) -> b#(x1)
    a#(a(a(x1))) -> b#(b(x1))
    a#(a(a(x1))) -> b#(b(b(x1)))
    a#(a(a(x1))) -> a#(b(b(b(x1))))
    b#(b(a(b(x1)))) -> a#(x1)
    b#(b(a(b(x1)))) -> a#(a(x1))
    b#(b(a(b(x1)))) -> a#(a(a(x1)))
   TRS:
    a(a(a(x1))) -> a(b(b(b(x1))))
    b(b(a(b(x1)))) -> a(a(a(x1)))
   graph:
    b#(b(a(b(x1)))) -> a#(a(a(x1))) ->
    a#(a(a(x1))) -> a#(b(b(b(x1))))
    b#(b(a(b(x1)))) -> a#(a(a(x1))) -> a#(a(a(x1))) -> b#(b(b(x1)))
    b#(b(a(b(x1)))) -> a#(a(a(x1))) -> a#(a(a(x1))) -> b#(b(x1))
    b#(b(a(b(x1)))) -> a#(a(a(x1))) -> a#(a(a(x1))) -> b#(x1)
    b#(b(a(b(x1)))) -> a#(a(x1)) -> a#(a(a(x1))) -> a#(b(b(b(x1))))
    b#(b(a(b(x1)))) -> a#(a(x1)) -> a#(a(a(x1))) -> b#(b(b(x1)))
    b#(b(a(b(x1)))) -> a#(a(x1)) -> a#(a(a(x1))) -> b#(b(x1))
    b#(b(a(b(x1)))) -> a#(a(x1)) -> a#(a(a(x1))) -> b#(x1)
    b#(b(a(b(x1)))) -> a#(x1) -> a#(a(a(x1))) -> a#(b(b(b(x1))))
    b#(b(a(b(x1)))) -> a#(x1) -> a#(a(a(x1))) -> b#(b(b(x1)))
    b#(b(a(b(x1)))) -> a#(x1) -> a#(a(a(x1))) -> b#(b(x1))
    b#(b(a(b(x1)))) -> a#(x1) -> a#(a(a(x1))) -> b#(x1)
    a#(a(a(x1))) -> b#(b(b(x1))) -> b#(b(a(b(x1)))) -> a#(a(a(x1)))
    a#(a(a(x1))) -> b#(b(b(x1))) -> b#(b(a(b(x1)))) -> a#(a(x1))
    a#(a(a(x1))) -> b#(b(b(x1))) -> b#(b(a(b(x1)))) -> a#(x1)
    a#(a(a(x1))) -> b#(b(x1)) -> b#(b(a(b(x1)))) -> a#(a(a(x1)))
    a#(a(a(x1))) -> b#(b(x1)) -> b#(b(a(b(x1)))) -> a#(a(x1))
    a#(a(a(x1))) -> b#(b(x1)) -> b#(b(a(b(x1)))) -> a#(x1)
    a#(a(a(x1))) -> b#(x1) -> b#(b(a(b(x1)))) -> a#(a(a(x1)))
    a#(a(a(x1))) -> b#(x1) -> b#(b(a(b(x1)))) -> a#(a(x1))
    a#(a(a(x1))) -> b#(x1) -> b#(b(a(b(x1)))) -> a#(x1)
    a#(a(a(x1))) -> a#(b(b(b(x1)))) ->
    a#(a(a(x1))) -> a#(b(b(b(x1))))
    a#(a(a(x1))) -> a#(b(b(b(x1)))) -> a#(a(a(x1))) -> b#(b(b(x1)))
    a#(a(a(x1))) -> a#(b(b(b(x1)))) -> a#(a(a(x1))) -> b#(b(x1))
    a#(a(a(x1))) -> a#(b(b(b(x1)))) -> a#(a(a(x1))) -> b#(x1)
   Arctic Interpretation Processor:
    dimension: 1
    usable rules:
     a(a(a(x1))) -> a(b(b(b(x1))))
     b(b(a(b(x1)))) -> a(a(a(x1)))
    interpretation:
     [b#](x0) = x0,
     
     [a#](x0) = 1x0,
     
     [b](x0) = 4x0,
     
     [a](x0) = 6x0
    orientation:
     a#(a(a(x1))) = 13x1 >= x1 = b#(x1)
     
     a#(a(a(x1))) = 13x1 >= 4x1 = b#(b(x1))
     
     a#(a(a(x1))) = 13x1 >= 8x1 = b#(b(b(x1)))
     
     a#(a(a(x1))) = 13x1 >= 13x1 = a#(b(b(b(x1))))
     
     b#(b(a(b(x1)))) = 14x1 >= 1x1 = a#(x1)
     
     b#(b(a(b(x1)))) = 14x1 >= 7x1 = a#(a(x1))
     
     b#(b(a(b(x1)))) = 14x1 >= 13x1 = a#(a(a(x1)))
     
     a(a(a(x1))) = 18x1 >= 18x1 = a(b(b(b(x1))))
     
     b(b(a(b(x1)))) = 18x1 >= 18x1 = a(a(a(x1)))
    problem:
     DPs:
      a#(a(a(x1))) -> a#(b(b(b(x1))))
     TRS:
      a(a(a(x1))) -> a(b(b(b(x1))))
      b(b(a(b(x1)))) -> a(a(a(x1)))
    Restore Modifier:
     DPs:
      a#(a(a(x1))) -> a#(b(b(b(x1))))
     TRS:
      a(a(a(x1))) -> a(b(b(b(x1))))
      b(b(a(b(x1)))) -> a(a(a(x1)))
     EDG Processor:
      DPs:
       a#(a(a(x1))) -> a#(b(b(b(x1))))
      TRS:
       a(a(a(x1))) -> a(b(b(b(x1))))
       b(b(a(b(x1)))) -> a(a(a(x1)))
      graph:
       a#(a(a(x1))) -> a#(b(b(b(x1)))) -> a#(a(a(x1))) -> a#(b(b(b(x1))))
      Arctic Interpretation Processor:
       dimension: 4
       usable rules:
        a(a(a(x1))) -> a(b(b(b(x1))))
        b(b(a(b(x1)))) -> a(a(a(x1)))
       interpretation:
        [a#](x0) = [-& 0  -& -&]x0 + [0],
        
                  [-& -& 0  0 ]     [0]
                  [-& -& -& 0 ]     [0]
        [b](x0) = [0  0  0  0 ]x0 + [0]
                  [0  0  -& -&]     [0],
        
                  [-& -& 1  1 ]     [1]
                  [0  -& 0  0 ]     [0]
        [a](x0) = [-& 0  0  -&]x0 + [0]
                  [-& -& 0  -&]     [0]
       orientation:
        a#(a(a(x1))) = [-& 0  1  1 ]x1 + [1] >= [-& -& 0  0 ]x1 + [0] = a#(b(b(b(x1))))
        
                      [1 1 1 1]     [1]    [1 1 1 1]     [1]                 
                      [0 1 1 0]     [1]    [0 0 0 0]     [0]                 
        a(a(a(x1))) = [0 0 1 1]x1 + [1] >= [0 0 0 0]x1 + [0] = a(b(b(b(x1))))
                      [0 0 0 0]     [0]    [0 0 0 0]     [0]                 
        
                         [1 1 1 1]     [1]    [1 1 1 1]     [1]              
                         [1 1 1 1]     [1]    [0 1 1 0]     [1]              
        b(b(a(b(x1)))) = [1 1 1 1]x1 + [1] >= [0 0 1 1]x1 + [1] = a(a(a(x1)))
                         [0 0 0 0]     [0]    [0 0 0 0]     [0]              
       problem:
        DPs:
         
        TRS:
         a(a(a(x1))) -> a(b(b(b(x1))))
         b(b(a(b(x1)))) -> a(a(a(x1)))
       Qed