/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

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

Proof:
 DP Processor:
  DPs:
   a#(a(a(b(x1)))) -> a#(x1)
   a#(a(a(b(x1)))) -> b#(a(x1))
   a#(a(a(b(x1)))) -> a#(b(a(x1)))
   a#(a(a(b(x1)))) -> b#(a(b(a(x1))))
   b#(b(a(x1))) -> a#(b(a(x1)))
   b#(b(a(x1))) -> a#(a(b(a(x1))))
  TRS:
   a(a(a(b(x1)))) -> b(a(b(a(x1))))
   b(b(a(x1))) -> a(a(b(a(x1))))
  TDG Processor:
   DPs:
    a#(a(a(b(x1)))) -> a#(x1)
    a#(a(a(b(x1)))) -> b#(a(x1))
    a#(a(a(b(x1)))) -> a#(b(a(x1)))
    a#(a(a(b(x1)))) -> b#(a(b(a(x1))))
    b#(b(a(x1))) -> a#(b(a(x1)))
    b#(b(a(x1))) -> a#(a(b(a(x1))))
   TRS:
    a(a(a(b(x1)))) -> b(a(b(a(x1))))
    b(b(a(x1))) -> a(a(b(a(x1))))
   graph:
    b#(b(a(x1))) -> a#(a(b(a(x1)))) ->
    a#(a(a(b(x1)))) -> b#(a(b(a(x1))))
    b#(b(a(x1))) -> a#(a(b(a(x1)))) ->
    a#(a(a(b(x1)))) -> a#(b(a(x1)))
    b#(b(a(x1))) -> a#(a(b(a(x1)))) -> a#(a(a(b(x1)))) -> b#(a(x1))
    b#(b(a(x1))) -> a#(a(b(a(x1)))) -> a#(a(a(b(x1)))) -> a#(x1)
    b#(b(a(x1))) -> a#(b(a(x1))) -> a#(a(a(b(x1)))) -> b#(a(b(a(x1))))
    b#(b(a(x1))) -> a#(b(a(x1))) -> a#(a(a(b(x1)))) -> a#(b(a(x1)))
    b#(b(a(x1))) -> a#(b(a(x1))) -> a#(a(a(b(x1)))) -> b#(a(x1))
    b#(b(a(x1))) -> a#(b(a(x1))) -> a#(a(a(b(x1)))) -> a#(x1)
    a#(a(a(b(x1)))) -> b#(a(b(a(x1)))) ->
    b#(b(a(x1))) -> a#(a(b(a(x1))))
    a#(a(a(b(x1)))) -> b#(a(b(a(x1)))) -> b#(b(a(x1))) -> a#(b(a(x1)))
    a#(a(a(b(x1)))) -> b#(a(x1)) -> b#(b(a(x1))) -> a#(a(b(a(x1))))
    a#(a(a(b(x1)))) -> b#(a(x1)) -> b#(b(a(x1))) -> a#(b(a(x1)))
    a#(a(a(b(x1)))) -> a#(b(a(x1))) ->
    a#(a(a(b(x1)))) -> b#(a(b(a(x1))))
    a#(a(a(b(x1)))) -> a#(b(a(x1))) ->
    a#(a(a(b(x1)))) -> a#(b(a(x1)))
    a#(a(a(b(x1)))) -> a#(b(a(x1))) -> a#(a(a(b(x1)))) -> b#(a(x1))
    a#(a(a(b(x1)))) -> a#(b(a(x1))) -> a#(a(a(b(x1)))) -> a#(x1)
    a#(a(a(b(x1)))) -> a#(x1) -> a#(a(a(b(x1)))) -> b#(a(b(a(x1))))
    a#(a(a(b(x1)))) -> a#(x1) -> a#(a(a(b(x1)))) -> a#(b(a(x1)))
    a#(a(a(b(x1)))) -> a#(x1) -> a#(a(a(b(x1)))) -> b#(a(x1))
    a#(a(a(b(x1)))) -> a#(x1) -> a#(a(a(b(x1)))) -> a#(x1)
   Arctic Interpretation Processor:
    dimension: 4
    usable rules:
     a(a(a(b(x1)))) -> b(a(b(a(x1))))
     b(b(a(x1))) -> a(a(b(a(x1))))
    interpretation:
     [b#](x0) = [1  -& -& -&]x0 + [0],
     
     [a#](x0) = [0  -& -& 0 ]x0 + [0],
     
               [-& -& -& 0 ]     [0 ]
               [-& -& -& 0 ]     [0 ]
     [a](x0) = [0  0  0  0 ]x0 + [0 ]
               [0  -& 0  -&]     [-&],
     
               [0  0  -& -&]     [0]
               [0  0  -& 1 ]     [1]
     [b](x0) = [0  0  -& -&]x0 + [0]
               [-& 0  -& -&]     [0]
    orientation:
     a#(a(a(b(x1)))) = [0  0  -& 1 ]x1 + [1] >= [0  -& -& 0 ]x1 + [0] = a#(x1)
     
     a#(a(a(b(x1)))) = [0  0  -& 1 ]x1 + [1] >= [-& -& -& 1 ]x1 + [1] = b#(a(x1))
     
     a#(a(a(b(x1)))) = [0  0  -& 1 ]x1 + [1] >= [-& -& -& 0 ]x1 + [0] = a#(b(a(x1)))
     
     a#(a(a(b(x1)))) = [0  0  -& 1 ]x1 + [1] >= [-& -& -& 1 ]x1 + [1] = b#(a(b(a(x1))))
     
     b#(b(a(x1))) = [-& -& -& 1 ]x1 + [1] >= [-& -& -& 0 ]x1 + [0] = a#(b(a(x1)))
     
     b#(b(a(x1))) = [-& -& -& 1 ]x1 + [1] >= [-& -& -& 0 ]x1 + [0] = a#(a(b(a(x1))))
     
                      [0  0  -& 1 ]     [1]    [-& -& -& 0 ]     [0]                 
                      [0  0  -& 1 ]     [1]    [-& -& -& 1 ]     [1]                 
     a(a(a(b(x1)))) = [0  0  -& 1 ]x1 + [1] >= [-& -& -& 0 ]x1 + [0] = b(a(b(a(x1))))
                      [0  0  -& 1 ]     [1]    [-& -& -& 0 ]     [0]                 
     
                   [1  -& 1  0 ]     [1]    [-& -& -& 0 ]     [0]                 
                   [1  -& 1  1 ]     [1]    [-& -& -& 0 ]     [0]                 
     b(b(a(x1))) = [1  -& 1  0 ]x1 + [1] >= [1  -& 1  0 ]x1 + [1] = a(a(b(a(x1))))
                   [1  -& 1  0 ]     [1]    [1  -& 1  0 ]     [1]                 
    problem:
     DPs:
      a#(a(a(b(x1)))) -> a#(x1)
      a#(a(a(b(x1)))) -> b#(a(x1))
      a#(a(a(b(x1)))) -> b#(a(b(a(x1))))
     TRS:
      a(a(a(b(x1)))) -> b(a(b(a(x1))))
      b(b(a(x1))) -> a(a(b(a(x1))))
    Restore Modifier:
     DPs:
      a#(a(a(b(x1)))) -> a#(x1)
      a#(a(a(b(x1)))) -> b#(a(x1))
      a#(a(a(b(x1)))) -> b#(a(b(a(x1))))
     TRS:
      a(a(a(b(x1)))) -> b(a(b(a(x1))))
      b(b(a(x1))) -> a(a(b(a(x1))))
     EDG Processor:
      DPs:
       a#(a(a(b(x1)))) -> a#(x1)
       a#(a(a(b(x1)))) -> b#(a(x1))
       a#(a(a(b(x1)))) -> b#(a(b(a(x1))))
      TRS:
       a(a(a(b(x1)))) -> b(a(b(a(x1))))
       b(b(a(x1))) -> a(a(b(a(x1))))
      graph:
       a#(a(a(b(x1)))) -> a#(x1) -> a#(a(a(b(x1)))) -> a#(x1)
       a#(a(a(b(x1)))) -> a#(x1) -> a#(a(a(b(x1)))) -> b#(a(x1))
       a#(a(a(b(x1)))) -> a#(x1) -> a#(a(a(b(x1)))) -> b#(a(b(a(x1))))
      SCC Processor:
       #sccs: 1
       #rules: 1
       #arcs: 3/9
       DPs:
        a#(a(a(b(x1)))) -> a#(x1)
       TRS:
        a(a(a(b(x1)))) -> b(a(b(a(x1))))
        b(b(a(x1))) -> a(a(b(a(x1))))
       Usable Rule Processor:
        DPs:
         a#(a(a(b(x1)))) -> a#(x1)
        TRS:
         
        Arctic Interpretation Processor:
         dimension: 1
         usable rules:
          
         interpretation:
          [a#](x0) = x0,
          
          [a](x0) = x0 + 0,
          
          [b](x0) = 5x0 + 8
         orientation:
          a#(a(a(b(x1)))) = 5x1 + 8 >= x1 = a#(x1)
         problem:
          DPs:
           
          TRS:
           
         Qed