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

Proof:
 DP Processor:
  DPs:
   b#(b(b(x1))) -> a#(x1)
   b#(b(b(x1))) -> a#(a(x1))
   b#(b(b(x1))) -> a#(a(a(x1)))
   a#(a(a(x1))) -> b#(x1)
   a#(a(a(x1))) -> a#(b(x1))
   a#(a(a(x1))) -> b#(a(b(x1)))
  TRS:
   b(b(b(x1))) -> a(a(a(x1)))
   a(a(a(x1))) -> b(a(b(x1)))
  TDG Processor:
   DPs:
    b#(b(b(x1))) -> a#(x1)
    b#(b(b(x1))) -> a#(a(x1))
    b#(b(b(x1))) -> a#(a(a(x1)))
    a#(a(a(x1))) -> b#(x1)
    a#(a(a(x1))) -> a#(b(x1))
    a#(a(a(x1))) -> b#(a(b(x1)))
   TRS:
    b(b(b(x1))) -> a(a(a(x1)))
    a(a(a(x1))) -> b(a(b(x1)))
   graph:
    a#(a(a(x1))) -> a#(b(x1)) -> a#(a(a(x1))) -> b#(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))) -> b#(a(b(x1))) -> b#(b(b(x1))) -> a#(a(a(x1)))
    a#(a(a(x1))) -> b#(a(b(x1))) -> b#(b(b(x1))) -> a#(a(x1))
    a#(a(a(x1))) -> b#(a(b(x1))) -> b#(b(b(x1))) -> a#(x1)
    a#(a(a(x1))) -> b#(x1) -> b#(b(b(x1))) -> a#(a(a(x1)))
    a#(a(a(x1))) -> b#(x1) -> b#(b(b(x1))) -> a#(a(x1))
    a#(a(a(x1))) -> b#(x1) -> b#(b(b(x1))) -> a#(x1)
    b#(b(b(x1))) -> a#(a(a(x1))) -> a#(a(a(x1))) -> b#(a(b(x1)))
    b#(b(b(x1))) -> a#(a(a(x1))) -> a#(a(a(x1))) -> a#(b(x1))
    b#(b(b(x1))) -> a#(a(a(x1))) -> a#(a(a(x1))) -> b#(x1)
    b#(b(b(x1))) -> a#(a(x1)) -> a#(a(a(x1))) -> b#(a(b(x1)))
    b#(b(b(x1))) -> a#(a(x1)) -> a#(a(a(x1))) -> a#(b(x1))
    b#(b(b(x1))) -> a#(a(x1)) -> a#(a(a(x1))) -> b#(x1)
    b#(b(b(x1))) -> a#(x1) -> a#(a(a(x1))) -> b#(a(b(x1)))
    b#(b(b(x1))) -> a#(x1) -> a#(a(a(x1))) -> a#(b(x1))
    b#(b(b(x1))) -> a#(x1) -> a#(a(a(x1))) -> b#(x1)
   Arctic Interpretation Processor:
    dimension: 1
    usable rules:
     b(b(b(x1))) -> a(a(a(x1)))
     a(a(a(x1))) -> b(a(b(x1)))
    interpretation:
     [a#](x0) = x0,
     
     [b#](x0) = x0,
     
     [a](x0) = 1x0,
     
     [b](x0) = 1x0
    orientation:
     b#(b(b(x1))) = 2x1 >= x1 = a#(x1)
     
     b#(b(b(x1))) = 2x1 >= 1x1 = a#(a(x1))
     
     b#(b(b(x1))) = 2x1 >= 2x1 = a#(a(a(x1)))
     
     a#(a(a(x1))) = 2x1 >= x1 = b#(x1)
     
     a#(a(a(x1))) = 2x1 >= 1x1 = a#(b(x1))
     
     a#(a(a(x1))) = 2x1 >= 2x1 = b#(a(b(x1)))
     
     b(b(b(x1))) = 3x1 >= 3x1 = a(a(a(x1)))
     
     a(a(a(x1))) = 3x1 >= 3x1 = b(a(b(x1)))
    problem:
     DPs:
      b#(b(b(x1))) -> a#(a(a(x1)))
      a#(a(a(x1))) -> b#(a(b(x1)))
     TRS:
      b(b(b(x1))) -> a(a(a(x1)))
      a(a(a(x1))) -> b(a(b(x1)))
    Restore Modifier:
     DPs:
      b#(b(b(x1))) -> a#(a(a(x1)))
      a#(a(a(x1))) -> b#(a(b(x1)))
     TRS:
      b(b(b(x1))) -> a(a(a(x1)))
      a(a(a(x1))) -> b(a(b(x1)))
     EDG Processor:
      DPs:
       b#(b(b(x1))) -> a#(a(a(x1)))
       a#(a(a(x1))) -> b#(a(b(x1)))
      TRS:
       b(b(b(x1))) -> a(a(a(x1)))
       a(a(a(x1))) -> b(a(b(x1)))
      graph:
       a#(a(a(x1))) -> b#(a(b(x1))) -> b#(b(b(x1))) -> a#(a(a(x1)))
       b#(b(b(x1))) -> a#(a(a(x1))) -> a#(a(a(x1))) -> b#(a(b(x1)))
      Arctic Interpretation Processor:
       dimension: 3
       usable rules:
        b(b(b(x1))) -> a(a(a(x1)))
        a(a(a(x1))) -> b(a(b(x1)))
       interpretation:
        [a#](x0) = [0  0  -&]x0 + [0],
        
        [b#](x0) = [-& 0  -&]x0 + [0],
        
                  [0  0  1 ]     [1]
        [a](x0) = [0  -& 0 ]x0 + [0]
                  [0  1  0 ]     [0],
        
                  [0 1 0]     [0 ]
        [b](x0) = [0 1 0]x0 + [0 ]
                  [0 1 0]     [-&]
       orientation:
        b#(b(b(x1))) = [1 2 1]x1 + [1] >= [1 2 1]x1 + [1] = a#(a(a(x1)))
        
        a#(a(a(x1))) = [1 2 1]x1 + [1] >= [0 1 0]x1 + [0] = b#(a(b(x1)))
        
                      [2 3 2]     [2]    [2 2 2]     [2]              
        b(b(b(x1))) = [2 3 2]x1 + [2] >= [1 2 1]x1 + [1] = a(a(a(x1)))
                      [2 3 2]     [2]    [1 2 2]     [2]              
        
                      [2 2 2]     [2]    [1 2 1]     [1]              
        a(a(a(x1))) = [1 2 1]x1 + [1] >= [1 2 1]x1 + [1] = b(a(b(x1)))
                      [1 2 2]     [2]    [1 2 1]     [1]              
       problem:
        DPs:
         b#(b(b(x1))) -> a#(a(a(x1)))
        TRS:
         b(b(b(x1))) -> a(a(a(x1)))
         a(a(a(x1))) -> b(a(b(x1)))
       Restore Modifier:
        DPs:
         b#(b(b(x1))) -> a#(a(a(x1)))
        TRS:
         b(b(b(x1))) -> a(a(a(x1)))
         a(a(a(x1))) -> b(a(b(x1)))
        EDG Processor:
         DPs:
          b#(b(b(x1))) -> a#(a(a(x1)))
         TRS:
          b(b(b(x1))) -> a(a(a(x1)))
          a(a(a(x1))) -> b(a(b(x1)))
         graph:
          
         SCC Processor:
          #sccs: 0
          #rules: 0
          #arcs: 0/1